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