Review materials on continuous systems II 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