spring semester 2006 ese 601: hybrid systems review materials on continuous systems ii
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![Page 1: Spring semester 2006 ESE 601: Hybrid Systems Review materials on continuous systems II](https://reader034.vdocuments.mx/reader034/viewer/2022051516/56649d4b5503460f94a28b9d/html5/thumbnails/1.jpg)
Spring semester 2006
ESE 601: Hybrid Systems
Review materials on continuous systems II
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Contents
• Controllability
• Observability
• Invariant subspace
• Controller design: controlled invariance
• Controller design: pole placement
![Page 3: Spring semester 2006 ESE 601: Hybrid Systems Review materials on continuous systems II](https://reader034.vdocuments.mx/reader034/viewer/2022051516/56649d4b5503460f94a28b9d/html5/thumbnails/3.jpg)
Reachability
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Reachability of linear systems
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Controllability
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Controllability
?
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Controllability
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Controllability
the inverse exists because of controllability
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Controllable subspace
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Controllable subspace
![Page 11: Spring semester 2006 ESE 601: Hybrid Systems Review materials on continuous systems II](https://reader034.vdocuments.mx/reader034/viewer/2022051516/56649d4b5503460f94a28b9d/html5/thumbnails/11.jpg)
Contents
• Controllability
• Observability
• Invariant subspace
• Controller design: controlled invariance
• Controller design: pole placement
![Page 12: Spring semester 2006 ESE 601: Hybrid Systems Review materials on continuous systems II](https://reader034.vdocuments.mx/reader034/viewer/2022051516/56649d4b5503460f94a28b9d/html5/thumbnails/12.jpg)
Observability
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Observability
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Observability
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Observability
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Observable subspace
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Observable subspace
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Contents
• Controllability
• Observability
• Invariant subspace
• Controller design: controlled invariance
• Controller design: pole placement
![Page 19: Spring semester 2006 ESE 601: Hybrid Systems Review materials on continuous systems II](https://reader034.vdocuments.mx/reader034/viewer/2022051516/56649d4b5503460f94a28b9d/html5/thumbnails/19.jpg)
Invariant subspace
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Invariant subspace
![Page 21: Spring semester 2006 ESE 601: Hybrid Systems Review materials on continuous systems II](https://reader034.vdocuments.mx/reader034/viewer/2022051516/56649d4b5503460f94a28b9d/html5/thumbnails/21.jpg)
Contents
• Controllability
• Observability
• Invariant subspace
• Controller design: controlled invariance
• Controller design: pole placement
![Page 22: Spring semester 2006 ESE 601: Hybrid Systems Review materials on continuous systems II](https://reader034.vdocuments.mx/reader034/viewer/2022051516/56649d4b5503460f94a28b9d/html5/thumbnails/22.jpg)
Controlled invariance
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Controlled invariance
Geometric interpretation
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Controlled invariance
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Controlled invariance
![Page 26: Spring semester 2006 ESE 601: Hybrid Systems Review materials on continuous systems II](https://reader034.vdocuments.mx/reader034/viewer/2022051516/56649d4b5503460f94a28b9d/html5/thumbnails/26.jpg)
Controlled invariance
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Contents
• Controllability
• Observability
• Invariant subspace
• Controller design: controlled invariance
• Controller design: pole placement
![Page 28: Spring semester 2006 ESE 601: Hybrid Systems Review materials on continuous systems II](https://reader034.vdocuments.mx/reader034/viewer/2022051516/56649d4b5503460f94a28b9d/html5/thumbnails/28.jpg)
Pole placement
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Pole placement
SYSTEM
Feedback controller
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Pole placement