Improved multiple Lyapunov functions of input–output-to-state stability for nonlinear switched systems

Abstract

This study is concerned with the Lyapunov characterization of input–output-to-state stability (IOSS) for time-varying nonlinear switched systems. Considering the restriction in current methods that each subsystem must be IOSS, and the Lyapunov function of each subsystem is strictly descended in the definition domain, in this work, by extending multiple Lyapunov functions to an indefinite form, the restriction on the negativity of the time derivative of Lyapunov functions is relaxed; additionally, all subsystems are permitted to not be IOSS in the state space. The results obtained are then extended to verifying the integral input–output-to-state stability (iIOSS) and output-to-state stability (OSS); and a state-norm estimator is proposed based on the indefinite Lyapunov function as a by-product. Finally, a numerical example illustrates the effectiveness of the results.