1. STABILITY of SWITCHED SYSTEMS – family of asymptotically stable systems – piecewise constant switching signal Want GUAS w.r.t. want GUES For switched linear system

2. SWITCHED LINEAR SYSTEMS: KNOWN RESULTS – Lie algebra spanned by matrices is nilpotent is solvable is solvable + compact GUES common quadratic Lyapunov function Otherwise, Lie algebra doesn’t provide enough information

3. SWITCHED NONLINEAR SYSTEMS: OPEN PROBLEM Commuting systems Linearization Problem: Which structural properties (if any) of the Lie algebra generated by a noncommuting family of asymptotically stable nonlinear vector fields guarantee stability of every corresponding switched system? Important special case: GUAS