Robust asymptotic stabilizability of Petersen´s counterexample via a linear static controller

A stabilizing linear static controller is discovered for a linear time-varying uncertain system of Petersen. We use the concept of a sandwich cone decomposition to show that Petersen´s system is stabilizable by linear static controllers. We establish the surprising result that Petersen´s system is stabilizable against time-varying uncertainties on any given compact subset of the uncertainty controllability space. Our work suggests the use of “scalar-quadratic” Lyapunov functions, a special subclass of polyhedral Lyapunov functions, in establishing stability for other linear time-varying uncertain systems, and it reopens the study of the conjecture: stabilizability via nonlinear control always implies stabilizability via linear control