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

?

the inverse exists because of controllability

Controllable subspace

Contents Controllability Observability Invariant subspace Controller design: controlled invariance Controller design: pole placement

Observability

Observable subspace

Contents Controllability Observability Invariant subspace Controller design: controlled invariance Controller design: pole placement

Invariant subspace

Contents Controllability Observability Invariant subspace Controller design: controlled invariance Controller design: pole placement

Controlled invariance

Geometric interpretation

Controlled invariance

Contents Controllability Observability Invariant subspace Controller design: controlled invariance Controller design: pole placement

Pole placement

SYSTEM Feedback controller

Pole placement