Stability of shuffled switched linear systems: A joint spectral radius approach

A switching signal for a switched system is said to be shuffled if all modes of the are activated infinitely often. In this paper, we develop tools analyze stability properties discrete-time linear systems driven by signals. We introduce new notion joint spectral radius (SJSR), which intuitively measures how much state contracts each time shuffles (i.e. have been activated). show relates associated systems. particular, that some unstable arbitrary signals can stabilized using shuffle sufficiently fast and SJSR allows us derive an expression minimal shuffling rate required stabilize system. then present several approaches compute lower upper bounds such as classical radius, Lyapunov functions finite automata. Several tightness results established. Finally, numerical experiments presented illustrate main paper.