Stability analysis of switched polynomial systems using dissipation inequalities

A polynomial approach to deal with stability analysis of polynomial switched systems, i.e., polynomial continuous systems with switching signals, using dissipation inequalities under arbitrary switching is presented. It is shown that the representation of the original switched problem into a continuous polynomial systems allows us to use the dissipation inequality for polynomial systems. With this method and from a theoretical point of view, we provide an alternative way to search for a common Lyapunov function for switched systems.