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Spring semester 2006
ESE 601: Hybrid Systems
Review materials on continuous systems II
Contents
• Controllability
• Observability
• Invariant subspace
• Controller design: controlled invariance
• Controller design: pole placement
Reachability
Reachability of linear systems
Controllability
Controllability
?
Controllability
Controllability
the inverse exists because of controllability
Controllable subspace
Controllable subspace
Contents
• Controllability
• Observability
• Invariant subspace
• Controller design: controlled invariance
• Controller design: pole placement
Observability
Observability
Observability
Observability
Observable subspace
Observable subspace
Contents
• Controllability
• Observability
• Invariant subspace
• Controller design: controlled invariance
• Controller design: pole placement
Invariant subspace
Invariant subspace
Contents
• Controllability
• Observability
• Invariant subspace
• Controller design: controlled invariance
• Controller design: pole placement
Controlled invariance
Controlled invariance
Geometric interpretation
Controlled invariance
Controlled invariance
Controlled invariance
Contents
• Controllability
• Observability
• Invariant subspace
• Controller design: controlled invariance
• Controller design: pole placement
Pole placement
Pole placement
SYSTEM
Feedback controller
Pole placement