2604.01429 Switched System Stability Under Arbitrary Switching Requires Common Lyapunov Functions: A Constructive Counterexample to Relaxed Conditions
Switched system stability under arbitrary switching requires common Lyapunov functions (CLFs). We construct an explicit counterexample---a family of 3 stable linear subsystems in $\mathbb{R}^4$ with pairwise CLFs but no common CLF---that diverges under a specific switching signal.