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