Improved Multiple Lyapunov Functions of input-to-output Stability and input-to-state Stability for Switched Systems

This paper investigates the Lyapunov characterizations of input-to-output stability (IOS) and input-to-state (ISS) for nonlinear switched systems. The restriction on negativity derivatives functions is relaxed; additionally, subsystems are not restricted to be ISS/IOS throughout state space. These problems overcome by a newly proposed method, which extends multiple (MLFs) an indefinite form. Indefinite (iMLFs) basis inequality estimate upper boundary system state. Moreover, we apply iMLFs method verify extended notions IOS in system. More relaxed sufficient conditions ISS proposed, simulation experiment carried out numerical example system, demonstrates their effectiveness superiority.