ivan vasil’evich gaishun (a tribute in honor of his sixtieth birthday)

ISSN 0012-2661, Differential Equations, 2006, Vol. 42, No. 10, pp. 1365–1373. c© Pleiades Publishing, Inc., 2006.Original Russian Text c© the Editorial Board, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 10, pp. 1299–1306.

MEMBERS OF SCIENTIFIC COMMUNITY

Ivan Vasil’evich Gaishun(A Tribute in Honor of His Sixtieth Birthday)

DOI: 10.1134/S0012266106100016

September 29, 2006 Ivan Vasil’evich Gaishun, a distinguishable scientist, an Academician of theNational Academy of Sciences of Belarus, a member of the European Academy of Sciences, Doctorof Sciences (physics and mathematics), a professor, a recognized specialist in differential equations,topological dynamics, and methods of mathematical modelling, celebrated his sixtieth birthday.

Gaishun was born in the village Petrovichi of Bobruiskii district in Mogilev region of Belarus.In 1964, after graduating from the Gorbatsevichi secondary school, he entered the MathematicalDivision at the Belarus State University. In 1969, he graduated from it with excellence, acquireda profession of mathematician, and was directed to the Institute for Mathematics of the Academyof Sciences of Belarus, where, till 1984, he worked as a probation researcher, a junior scientist,and a senior scientist at the Laboratory of Theory of Control Processes. Gaishun defended hisphilosophy doctor dissertation in 1972 and his doctoral dissertation at the Institute for Mathematicsand Mechanics of the Ural Division of the Academy of Sciences of USSR in 1984. In December,1984, Ivan Vasil’evich Gaishun was elected Head of the Laboratory of Mathematical Modelling andSystem Analysis, which was renamed in 1993 as the Division of Mathematical Theory of Systemsand is still headed by Gaishun. Since May, 1997 until April, 2002, he was Vice-President of theNational Academy of Sciences of Belarus, and since 1992 until now, he is Director of the Institutefor Mathematics of the National Academy of Sciences of Belarus. Since 1994 until now, he readslectures to students of Belarus State University as Professor of the Chair of Applied and TheoreticalMechanics at the Mechanical-Mathematical Division.

Ivan Vasil’evich Gaishun started his scientific activity already in student years, when he, underthe supervision by Barbashin, performed investigations on the stability of solutions of systemsof nonlinear differential equations. As a result of these investigations, he developed methods forthe construction of Lyapunov functions, which permit one to solve the well-known problem of theabsolute stability in a number of cases and can be used in the description of attraction domains ofequilibria of mechanical systems, periodic solutions of differential equations, and stability conditions

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for systems with random parameters. A number of these results was represented by Barbashin inhis monograph Funktsii Lyapunova (Lyapunov Functions, Moscow, 1970).

Later Gaishun’s field of scientific interests became much wider. It is mainly related to thedevelopment of the theory of dynamical systems treated in the wide sense and primarily to itsmodern directions such as completely integrable systems on manifolds; equations in total derivativesin Banach and locally convex topologically spaces; many-dimensional, many-parameter, and fuzzydynamical systems; systems of equations with a variable structure and delay systems; controlledcontinuous and discrete linear dynamical systems considered together with various topological andalgebraic structures (locally compact groups, rings, topological fields and bodies).

In each of these directions of mathematics, Gaishun obtained basic results among which thereare the development of stability theory for invariant sets on the basis of the notion of a filterin general topology; a deep generalization of the theory of Lyapunov characteristic numbers tononstationary linear total differential equations in Banach spaces; criteria for the boundedness,periodicity, and almost periodicity of total differential equations on locally convex spaces. Theseresults and a number of other important investigations, for example, foundations of the theory ofcompletely solvable discrete systems, were published in the monographs Vpolne razreshimye mno-gomernye differentsial’nye uravneniya (Completely Integrable Multidimensional Differential Equa-tions, Minsk, 1983) and Lineinye uravneniya v polnykh proizvodnykh (Linear Total DifferentialEquations, Minsk, 1989).

In theory of fuzzy sets, Ivan Vasil’evich Gaishun introduced the definition of a fuzzy dynamicalsystem (an F-system) on the basis of the original interpretation of Zadeh’s membership function andperformed a complete investigation of the stability (with respect to some filter with the propertyof invariance) of fuzzy points of F-systems. Gaishun also defined controlled linear systems in fuzzyspaces and found stability and controllability criteria for such systems. A number of Gaishun’spapers deal with the fundamental problem of modelling with the use of discrete systems distributedin the space of evolution processes; there he defined discrete systems with variable structure andinvestigated their properties of stability, controllability, and embedding.

A large cycle of Gaishun’s investigations on linear control theory was represented in the mono-graphs Mnogoparametricheskie sistemy upravleniya (Many-Parameter Control Systems, Minsk,1996), Vvedenie v teoriyu lineinykh nestatsionarnykh sistem (Introduction to Theory of LinearNonstationary Systems, Minsk, 1999), and Sistemy s diskretnym vremenem (Systems with DiscreteTime, Minsk, 2001).

Methods of qualitative theory for classes of many-parameter discrete control systems, includingthe class of 2D systems widely used in applications, were developed in the monograph Mnogopara-metricheskie sistemy upravleniya (Many-Parameter Control Systems). Somewhat later, the resultsobtained by Gaishun in theory of 2D systems were generalized to the much wider class of linearsystems defined in spaces of functions on topological commutative groups.

Two monographs, Vpolne razreshimye mnogomernye differentsial’nye uravneniya (CompletelyIntegrable Multidimensional Differential Equations, Minsk, 1983) and Vvedenie v teoriyu lineinykhnestatsionarnykh sistem (Introduction to Theory of Linear Nonstationary Systems, Minsk, 1999)were re-published by the Russian publishing company Editorial URSS (Moscow, 2004). IvanVasil’evich Gaishun is the author of more than 200 scientific publications and 5 monographs.

At present, Gaishun is active in the field of mathematical control theory. He developed newmethods for the investigation of the robustness property, stability, stabilizability, controllability,and observability of various classes of linear dynamical systems on the basis of ideas of modernalgebra, functional analysis, and topological dynamics. In particular, the classification of the setof linear controlled systems with respect to actions of various transformation groups in the systemstate space is one of the key problems in mathematical systems theory. Such problems go back tothe studies by Lyapunov, Perron, and Erugin on the asymptotic stability of linear nonstationarydifferential systems. Ivan Vasil’evich Gaishun developed a method for constructing canonical formsof linear nonstationary differential and discrete control systems, which permits one to obtain asolution of the above-mentioned classification problem in a number of important cases.

Theory and practice of total differential equations play an important role in Gaishun’s scientificactivity until now. In recent papers, he defined Hamiltonian linear and quasilinear systems in totaldifferentials, and for the above-mentioned class of systems with periodic coefficients, he derived sta-bility criteria and conditions for the strong stability, that is, conditions for stability to be stable un-der small perturbations of parameters preserving the total integrability and the Hamiltonian prop-erty of the system. Gaishun also developed the observability theory of linear nonstationary total

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differential systems, proved the maximum principle for a class of such systems, and developed a con-struction method for the minimum implementations of linear stationary total differential systems.

Note that Gaishun’s theoretical investigations have found straightforward applications in variousfields of science and technology; for example, total differential equations are widely used in quan-tum field theory, statistical mechanics, and theory of turbulence. The results on many-dimensionaland controlled systems are straightforwardly related to problems of analysis and synthesis of auto-mated regulation systems, digital processing of multidimensional signals, and cryptography. A num-ber of papers of straightforward economical value were performed under supervision by Gaishun.

Ivan Vasil’evich Gaishun successfully combines scientific research with teaching activity. Since1994, as Professor of the Chair “Applied and Theoretical Mechanics” of the Mechanical-Mathemat-ical Division of Belarus State University, he reads the lecture courses “Stability and Stabilizationof Dynamical Systems” and “Automated Control” and generously and frankly shares his accu-mulated experience and knowledge with youth. He often heads the State Examining Board onthe Mechanical-Mathematical Division, is a scientific supervisor of students writing term papersand degree works. Ivan Vasil’evich Gaishun feels responsible for the education of young scientists;he devotes much of his time to training high-skilled scientists and conserving and extending bestscientific traditions. He is an authoritative teacher, is respectful to his students, and surprisinglycombines kind-heartedness, understanding, and insistence on high standards. He has taught 6 phi-losophy doctors and 3 doctors of sciences in physics and mathematics, and he is one of authors ofthe teaching book in higher mathematics published in 2005.

Ivan Vasil’evich Gaishun gives much effort to scientific-organizational activity in the frameworkof the National Academy of Sciences of Belarus. He is President of the Belarus Mathematical Societyand member of the Presidium of the Higher Certifying Commission of Belarus, and for a long time,he has been member of the Council of the Belarus Republic Foundation for Basic Research. Now heis member of the Presidium of the National Academy of Sciences of Belarus, member of the EditorialBoards of the journals Differentsial’nye Uravneniya (Differential Equations), Doklady NAN Belarusi(Reports of the National Academy of Sciences of Belarus), and Computational Methods in AppliedMathematics, and head of a scientific seminar on mathematical theory of systems on which tens ofdissertations were represented.

Gaishun is widely known in the world-wide scientific society. He is member of the EuropeanAcademy of Sciences and the American Mathematical Society; he participates in numerous inter-national congresses, conferences, and schools, and collaborates with mathematical centers of manycountries.

Ivan Vasil’evich Gaishun was awarded the Prize of the commission of the Council of Ministers ofUSSR for the development and implementation of a special theme (1981), a diploma of the Councilof Ministers for high achievements in scientific activity (1996), and the State Prize of RepublicBelarus for the cycle of works “Investigation of Asymptotic Properties of Differential and DiscreteSystems” (2000).

Ivan Vasil’evich Gaishun is a gifted and powerful scientist with an inexhaustible amount of ideas,he has high humane qualities such as benevolence and adherence to principle, he creates a verykind and creative situation, and he always remains a sensitive and proper manager.

We congratulate Ivan Vasil’evich Gaishun with his birthday and wish him health and realizationof all his creative ideas.

Arutyunov, A.V., Emel’yanov, S.V., Izobov, N.A.,Il’in, V.A., Korovin, S.K., Korzyuk, V.I.,

Samoilenko, A.M., Borukhov, V.T., Kostyukova, O.I.,Shemyakina, T.K., and Yurchuk, N.I.

LIST OF I. V. GAISHUN’S PUBLICATIONS1

1997

139. Nikolai Pavlovich Erugin (A Tribute in Honor of His 90th Birthday) (together with Andreev, A.F.,Gromak, V.I., Izobov, N.A., Il’in, V.A., et al.), Differ. Uravn., vol. 33, no. 5, pp. 579–582.

140. Limit Points in a Filter and Stability of Dynamical Systems, Vestn. Vitebsk. Univ., no. 1, pp. 44–48.

1 For the beginning of the list see Differentsial’nye Uravneniya, 1977, vol. 36, no. 6, pp. 723–736.



141. Discrete Equations with a Variable Structure and Stability of Their Solutions, Differ. Uravn., vol. 33,no. 12, pp. 1607–1614.

142. Stability of Volterra Discrete Processes with Decreasing Aftereffect, Avtomat. i Telemekh., no. 6,pp. 118–124.

143. Factorization of Transition Operators and Structure of Infinite Zeros of Infinite-Dimensional LinearDynamic Systems (together with Borukhov, V.T.), Dokl. Nats. Akad. Nauk Belarusi , vol. 41, no. 4,pp. 5–9.

144. Discrete Equations with Varying Structure and Quadratic Optimization Problem for Linear VolterraEquation (together with Dymkov, M.P.), in Control Theory, Modeling and Simulation, Domek, S.,Emizsajlow, Z., and Kuszynski, R., Eds., Warsaw, Poland: Papers, vol. 1, pp. 123–128.

1998

145. Anatolii Mikhailovich Samoilenko (A Tribute in Honor of His 60th Birthday) (together withBoichuk, A.A., Izobov, N.A., Il’in, V.A., et al.), Differ. Uravn., vol. 34, no. 1, pp. 3–4.

146. Stabilization of Volterra Discrete Equations, Differ. Uravn., vol. 34, no. 2, pp. 272–278.

147. Controllability of Linear Time-Dependent Systems in the Class of Finite-Order Generalized Functions(together with Astrovskii, A.I.), Izv. RAN. Teor. Sist. Upravl., no. 2, pp. 24–30.

148. Stabilization of Trajectory by Sampled-Data Controls in the Case of Noises, Dokl. Akad. NaukBelarusi , vol. 42, no. 2, pp. 5–7.

149. Synthesis of G-Reducible Linear Nonstationary Systems, Dokl. Nats. Akad. Navuk. Belarusi , vol. 42,no. 3, pp. 5–8.

150. Existence of Canonical Forms of Linear Nonstationary Control Systems with Respect to an ExponentialGroup, Differ. Uravn., vol. 34, no. 6, pp. 727–734.

151. Uniform and Approximative Observability of Linear Nonstationary Systems (together with Astrov-ski, A.I.), Avtomat. i Telemekh., no. 7, pp. 3–13.

152. Topological Properties of Discrete 2-D Control Systems, The First International Workshop on Multi-dimensional (n-D) systems (Zielona Gora, Poland): Abstracts , pp. 98–99.

153. A Remark on the Control for the Spectrum of a Linear Nonstationary System, in Chetvertaya krym-skaya mezhdunar. mat. shkola “Metod funktsii Lyapunova i ego prilozheniya” (Alushta): Tez. dokl.(Abstr. 4th Crimean Int. Math. School “Method of Lyapunov Functions and Its Applications”,Alushta), p. 20.

154. Stability and LQ-Optimization Problems for Discrete Volterra Equations (together withDymkov, M.P.), Proc. IMACS-IEEE Conference “Comp. Eng. In Syst. Appl.” (CESA-98).(Tynisia): Papers, vol. 2, pp. 264–267.

155. Controllability, Stability and Stabilizability Problems for Continous-Discret 2-D Systems, J. of Electro-technics and Mathematics , no. 1, pp. 1–6.

156. Investigations at the Institute for Mathematics of the National Academy of Sciences of Belarus onDifferential Equations and Many-Parameter Systems (together with Izobov, N.A.), Vestsi Nats. Akad.Navuk Belarusi. Ser. Fiz.-Mat. Navuk , no. 4, pp. 5–19.

157. Canonical Forms, Control for Lyapunov Exponents, and Stabilization of Linear Nonstationary Sys-tems, Izv. Akad. Nauk. Teor. Sist. Upravl., no. 6, pp. 24–32.

158. Valentin Vladimirovich Murav’ev (A Tribute in Honor of His 60th Birthday) (together with Olekh-novich, N.M., Pilipovich, V.A., et al.), Vestsi Nats. Akad. Navuk Belarusi. Ser. Fiz.-Mat. Navuk ,no. 1, pp. 137–138.

1999

159. Controllability of Characteristic Vectors of Linear Nonstationary Systems, Differ. Uravn., vol. 35,no. 1, pp. 24–29.



160. Canonical Forms of Linear Nonstationary Control Systems with Respect to Various TransformationGroups, Avtomat. i Telemekh., no. 2, pp. 11–18.

161. Aleksandr Andreevich Samarskii (A Tribute in Honor of His 80th Birthday) (together with Abra-shin, V.N., Arsen’ev, A.A., Gulin, A.V., Emel’yanov, S.V., Il’in, V.A., et al.), Differ. Uravn., vol. 35,no. 2, pp. 147–149.

162. Multidimensional Discrete Systems of Variable Structure (together with Dymkov, M.P.), Mat. konf.“Eruginskie chteniya - VI” (Gomel’): Tez. dokl. (Abstr. Math. Conf. “Erugin Readings-VI” (Gomel,Belarus)), p. 85.

163. On the Embedding of Nonlinear Discrete Equations in Linear Systems (together with Borukhov, V.T.),Mat. konf. “Eruginskie chteniya-VI” (Gomel’): Tez. dokl. (Abstr. Math. Conf. “Erugin Readings-VI” (Gomel, Belarus)), p. 145.

164. On the Mathematical Creative Work of Petr Petrovich Zabreiko (together with Gorokhovik, V.V. andLebedev, A.V.), Tr. Inst. Mat. Nats. Akad. Nauk Belarusi , vol. 2, pp. 6–29.

165. On Canonical Forms of Linear Nonstationary Control Systems, Tr. Inst. Mat. Nats. Akad. NaukBelarusi , vol. 2, pp. 58–62.

166. Vvedenie v teoriyu lineinykh nestatsionarnykh sistem (Introduction to Theory of Linear NonstationarySystems), Minsk: Inst. Math. NAS Belarus.

167. Canonical Forms of Linear Discrete Two-Parameter Systems, Differ. Uravn., vol. 35, no. 7,pp. 964–968.

168. Petr Petrovich Zabreiko (A Tribute in Honor of His 60th Birthday) (together with Gorokhovik, V.V.,Izobov, N.A., Rogozin, S.V., et al.), Vestn. Belar. Gos. Univ. Ser. 1. Fiz. Mat. Inform., no. 2,pp. 76–77.

169. Embedding of Nonlinear Discrete Equations with a Varying Structure in Linear Systems (togetherwith Borukhov, V.T.), Differ. Uravn., vol. 35, no. 9, pp. 1207–1215.

170. Vladimir Mikhailovich Millionshchikov (A Tribute in Honor of His 60th Birthday) (together withAnosov, D.V., Vladimirov, V.S., Izobov, N.A., Il’in, V.A., et al.), Differ. Uravn., vol. 35, no. 10,pp. 1299–1302.

171. Stability of Multi-Dimensional Systems with Varying Structure (together with Dymkov, M.P.), Int.J. Math. and Comp. Sci., vol. 9, no. 4, pp. 101–110.

172. Synthesis of Linear Discrete Systems with Almost Periodic Solutions, Dokl. Nats. Akad. NavukBelarusi , vol. 43, no. 6, pp. 5–7.

2000

173. Asymptotic Estimation of States of Linear Nonstationary Discrete Systems, Tr. Inst. Mat. NANBelarusi , vol. 4, pp. 25–28.

174. Nikolai Alekseevich Izobov (A Tribute in Honor of His 60th Birthday) (together with Bibikov, Yu.N.,Vetokhin, A.N., Grin’, A.A., et al.), Tr. Inst. Mat. NAN Belarusi , vol. 4, pp. 3–8.

175. Nikolai Alekseevich Izobov (A Tribute in Honor of His 60th Birthday) (together with Abrashin, V.N.,Il’in, V.A., Kiguradze, I.T., et al.), Differ. Uravn., vol. 36, no. 1, pp. 3–6.

176. Uniformly Observable Nonstationary Systems with Many Outputs and Their Canonical Forms(together with Astrovskii, A.I.), Differ. Uravn., vol. 36, no. 1, pp. 18–25.

177. Canonical Forms of Linear Discrete Control Systems and Some of Their Applications, Avtomat. iTelemekh., no. 2, pp. 35–44.

178. Composite Linear Discrete Systems (together with Dymkov, M.P.), Vos’maya Belorusskaya mat. konf.(Minsk): Tez. dokl. (Abstr. VIII Belarus Math. Conf. (Minsk)), part 4, p. 61.



179. Multipass Continuous-Discrete Systems – Control Theory (together with Dymkov, M.P.), in TheSecond International Workshop Multidimensional (n-D) Systems (Zielona Gora, Poland): Abstracts ,pp. 231–235.

180. Proper Multidimensional Discrete Systems and Their Canonical Forms, Dokl Nats. Akad. NavukBelarusi , vol. 44, no. 3, pp. 5–7.

181. Canonical Form of Reducible Discrete Systems with Degenerate Coefficient Matrix, Differ. Uravn.,vol. 36, no. 7, pp. 939–945.

182. Controllability of Systems Governed by Linear Discrete Volterra Equations (together withDymkov, M.P.), Avtomat. i Telemekh., no. 7, pp. 88–100.

183. Control Problems for Multipass Continuous-Discrete Systems (together with Dymkov, M.P. et al.), inIV Int. Workshop “Control and Math.” (Poland): Abstracts , pp. 15–18.

184. Controllability of Discrete Linear Repetitive Processes – a Volterra Operator Approach (together withDymkov, M.P.), in CD ROM Proceeding of 15 Int. Sym. of Math. Theory of Networks and Syst.(France): Papers, pp. 19–26.

185. Control Problem for Discrete Volterra Systems, CD ROM Proceeding of 15 Int. Sym. of Math. Theoryof Networks and Syst. (France): Papers, pp. 31–37.

186. Linear Differential Systems with a Variable Structure (together with Borukhov, V.T.), Dokl. Nats.Akad. Navuk Belarusi , vol. 44, no. 5, pp. 30–33.

187. Vladimir Ivanovich Zubov (A Tribute in Honor of His 70th Birthday) (together with Gabasov, R.F.,Gorokhovik, V.V., Izobov, N.A., et al.), Differ. Uravn., vol. 36, no. 10, pp. 1299–1300.

188. Linear Systems with a Variable Structure. Controllability and Observability, Differ. Uravn., vol. 36,no. 11, pp. 1544–1549.

189. Canonical Forms of Linear Discrete Systems and Their Applications, in Mezhdunar. mat. konf.“Differentsial’nye uravneniya i sistemy komp’yuternoi algebry” (Brest): Tez. dokl. (Abstr. Int.Math. Conf. “Diff. Eqs. and Systems of Computer Algebra” (Brest, Belarus)), p. 15.

190. A Volterra Operator Based Observability Theory for Discrete Linear Repetetive Processes (togetherwith Dymkov, M. and Rogers, E.), Proceed. of 6-th International Conference Control, Automatics,Robastic and Vision, Singapure, p. 8.

2001

191. The Use of Canonical Forms of Linear Control Systems for the Stabilization of Periodic Solutions, Izv.Akad. Nauk. Teor. Sist. Upravl., no. 1, pp. 23–28.

192. Minimum Implementation of Two-Parameter Discrete-Continuous Systems (together with Goryach-kin, V.V.), Dokl. Nats. Akad. Navuk Belarusi , vol. 45, no. 1, pp. 45–47.

193. Anatolii Andreevich Martynyuk (A Tribute in Honor of His 60th Birthday) (together withAzbelev, N.V., Born, P., Vuichich, V.A., et al.), Differ. Uravn., vol. 37, no. 3, pp. 291–298.

194. Stability and Controllability of Composite Discrete (2-D) Systems (together with Dymkov, M.P.), Zh.Vychisl. Mat. Mat. Fiz., vol. 41, no. 4, pp. 577–594.

195. On the Reducibility of Linear Piecewise Smooth Systems with a Single Input to Hessenberg andFrobenius Forms (together with Borukhov, V.T.), Differ. Uravn., vol. 37, no. 4, pp. 446–452.

196. Yurii Petrovich Popov (A Tribute in Honor of His 60th Birthday) (together with Abrashin, V.N.,Galanin, N.P., Gulin, A.V., et al.), Differ. Uravn., vol. 37, no. 5, pp. 579–581.

197. Discrete Linear Repetitive Processes (together with Dymkov, M.P., Rogers, E., and Galkowski, K.),in Mat. konf. “Eruginskie chteniya - VII” (Grodno): Tez. dokl. (Abstr. Math. Conf. “EruginReadings-VII” (Grodno, Belarus), p. 65.

198. Control Problems for a Class of 2-D Repetitive Systems (together with Dymkov, M.P.), in The Inter-national Confer. “AMADE-2001” (Minsk): Abstracts , pp. 34–35.



199. Stabilization of Periodic Solutions of Discrete Control Systems, Izv. Akad. Nauk. Teor. Sist. Upravl.,no. 3, pp. 60–65.

200. Sistemy s diskretnym vremenem (Systems with a Discrete Time), Minsk.

201. Stability of a Class of 2-D Discrete Linear Repetitive Systems (together with Dymkov, M., Galkow-ski, K., Rogers, E., and Owens, D.H.), Proceed. of European Congress on Control (Portugal): Papers,pp. 1410–1415.

202. Estimation of States of Two-Parameter Discrete Systems, Differ. Uravn., vol. 37, no. 12,pp. 1674–1679.

203. On the Observability Properties of a Class of 2D Discrete Linear Systems (together with Dymkov, M.,Rogers, E., Galkowski, K., and Owens, D.H.), Proceed. of the 40 th IEEE Conference on Decision andControl (USA): Papers, pp. 3625–3630.

204. Control Structure in LQ-Optimization Problem for Discrete Process (together with Dymkov, M.),Proceed. of 1st IFAC/IEEE Symposium of system structure and control (Czech. Republic): Papers,pp. 65–71.

2002

205. Stabilization of a Periodic Solution of a Discrete System on a Ring, Dokl. Nats. Akad. Navuk Belarusi ,vol. 46, no. 1, pp. 41–43.

206. Linear-Quadratic Optimization Problem for Composite Discrete 2-D Control Systems (together withDymkov, M.P.), Avtomat. i Telemekh., no. 2, pp. 71–83.

207. Anatolii Borisovich Antonevich (A Tribute in Honor of His 60th Birthday) (together with Bernik, V.I.,Gorin, E.A., Zabreiko, P.P., et al.), Vestn. Belarus. Gos. Univ. Ser. 1. Fiz., Mat., Inform., no. 1,pp. 112–113.

208. Stabilization of Discrete Systems on Rings, Avtomat. i Telemekh., no. 3, pp. 37–45.

209. Synthesis of Stable Discrete Systems Defined on Arbitrary Fields, Differ. Uravn., vol. 38, no. 6,pp. 836–841.

210. Periodicity of Solutions of Two-Parameter Discrete Systems on Finite Fields, Differ. Uravn., vol. 38,no. 7, pp. 949–954.

211. Stabilization of Two-Parameter Discrete Systems Defined on Finite Fields, Izv. Ross. Akad. Nauk.Teor. Sist. Upravl., no. 3, pp. 71–76.

212. Nikolai Iosifovich Yurchuk (A Tribute in Honor of His 60th Birhday) (together with Kozulin, A.V.,Abrashin, V.N., Amel’kin, V.V., et al.), Vestn. Belarus. Gos. Univ. Ser. 1. Fiz. Mat. Inform.,no. 2, pp. 114–155.

213. Stability of Two-Parameter Discrete Systems Defined on Topological Fields, Dokl. Nats. Akad. NavukBelarusi , vol. 46, no. 4, pp. 27–29.

214. Nikolai Viktorovich Azbelev (A Tribute in Honor of His 80th Birthday) (together with Izobov, N.A.,Il’in, V.A., Kiguradze, I.T., et al.), Differ. Uravn., vol. 38, no. 7, pp. 867–869.

215. Aleksei Vladimirovich Gulin (A Tribute in Honor of His 60th Birthday) (together with Abrashin, V.N.,Izobov, N.A., Il’in, V.A., et al.), Differ. Uravn., vol. 38, no. 7, pp. 870–871.

216. Exponential Stability of Discrete Linear Repetetive Processes (together with Dymkov, M., Galkow-ski, K., Rogers, E., and Owens, D.H.), Int. J. Control , vol. 75, no. 12, pp. 861–869.

217. Some Properties of Linear Nonstationary Discrete Systems Defined on Rings, Differ. Uravn., vol. 38,no. 11, pp. 1540–1548.

218. Two-Parameter Discrete Systems on a Ring of Residues and Some of Their Properties, Avtomat. iTelemekh., no. 11, pp. 24–31.



2003

219. Synthesis of Nilpotent Two-Parameter Discrete Systems on a Commutive Ring, Differ. Uravn., vol. 39,no. 2, pp. 253–260.

220. Minimum Implementation of Completely Solvable Linear Differential Observation Systems (togetherwith Goryachkin, V.V.), Avtomat. i Telemekh., no. 3, pp. 52–60.

221. Z-Transform and Volterra-Operator Based Approaches to Controllability and Observability Analysisfor Discrete Linear Repetitive Processes (together with Dymkov, M., Rogers, E., Galkovski, K., andOwens, D.H.), Multidimens. Systems Signal Process., vol. 14, no. 4, pp. 365–395.

222. Synthesis of Nonstationary Linear Discrete Systems with an Aperiodic Reaction of State, Izv. Ross.Akad. Nauk. Teor. Sist. Upravl., no. 5, pp. 51–55.

223. Nikolai Antonovich Bobylev (Obituary Notice) (together with Emel’yanov, S.V., Izobov, N.A.,Il’in, V.A., et al.), Differ. Uravn., vol. 39, no. 4, pp. 570–572.

224. Observable Linear Nonstationary Total Differential Systems, Differ. Uravn., vol. 39, no. 10,pp. 1299–1306.

2004

225. Remarks on Observable Total Differential Equations, Avtomat. i Telemekh., no. 1, pp. 14–22.

226. Invariant Subspaces and Invariance Under Perturbations of Two-Parameter Discrete Systems, Dokl.Nats. Akad. Navuk Belarusi , vol. 48, no. 1, pp. 32–34.

227. Synthesis of Nilpotent Linear Discrete Systems on a Commutive Ring, Vestn. Fonda Fundam. Issled.,no. 1, pp. 77–79.

228. Controllability and Stabilization of Discrete Systems in the Space of Functions on a Finite CommutiveGroup with Values in a Commutive Ring, Izv. Ross. Akad. Nauk. Teor. Sist. Upravl., no. 3, pp. 7–12.

229. Controllability and Stabilization of Discrete Systems in the Space of Functions on a CommutiveSemigroup, Differ. Uravn., vol. 40, no. 6, pp. 816–824.

230. Observability Conditions for General Linear Systems, Differ. Uravn., vol. 40, no. 11, pp. 1532–1539.

231. Observability and Identification of States of a Two-Parameter Discrete System on a Commutive Ring,Avtomat. i Telemekh., no. 11, pp. 122–130.

232. Vvedenie v teoriyu lineinykh nestatsionarnykh sistem (Introduction to Theory of Linear NonstationarySystems), Moscow: Editorial URSS, 2nd ed.

233. Vpolne razreshimye mnogomernye differentsial’nye uravneniya (Completely Solvable MultidimensionalDifferential Equations), Moscow: Editorial URSS, 2nd ed.

2005

234. Stability of Linear Hamiltonian Total Differential Systems with Periodic Coefficients, Differ. Uravn.,vol. 41, no. 1, pp. 33–40.

235. Strong Stability of Linear Hamiltonian Total Differential Systems with Periodic Coefficients, Differ.Uravn., vol. 41, no. 6, pp. 739–745.

236. Investigation of Some Problems of Mathematical System Theory for Multi-Step Processes, Izv Ross.Akad. Nauk. Teor. Sist. Upravl., no. 2, pp. 5–9.

237. Asymptotic Properties of Some Class of Discrete Nonstationary Systems with Nonnegative Coefficients,Avtomat. i Telemekh., no. 9, pp. 3–11.

238. Vysshaya matematika dlya ekonomistov (Higher Mathematics for Economists) (together withMinyuk, S.A., Shevchenko, L.I., Bel’ko, I.V., and Kuz’mich, K.K.), Minsk: Belarus State Econ. Univ.



239. Minimum Implementation of Linear Observation Total Differential Systems with a Piecewise Contin-uous Input (together with Goryachkin, V.V.), in Mat. konf. “Eruginskie chteniya – X” (Mogilev):Tez. dokl. (Abstr. Math. Conf. “Erugin Readings-X” (Mogilev, Belarus)), p. 103.

240. Maximum Principle for Linear Control Total Differential Systems with a One-Parameter Input,Avtomat. i Telemekh., no. 12, pp. 31–39.

2006

241. Stability and Strong Stability of Quasistationary Linear Hamiltonian Total Differential Systems withPeriodic Coefficients, Differ. Uravn., vol. 42, no. 2, pp. 159–167.

242. Group of Linear Hamiltonian Total Differential Systems and Strong Stability of Its Stationary andPeriodic Elements, Differ. Uravn., vol. 42, no. 6, pp. 731–740.


ivan vasil’evich gaishun (a tribute in honor of his sixtieth birthday)

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