Indefinite Lyapunov functions based stability of switched nonlinear systems

This paper investigates the stability of switched nonlinear systems using indefinite Lyapunov functions, which mean that the derivation along the systems is indefinite. Two cases are considered: (i) the uniformly stable functions of the Lyapunov functions of all subsystems are integrally bounded, and (ii) the uniformly stable functions of the Lyapunov functions of part subsystems are integrally bounded. First, multiple Lyapunov-Krasovskii functionals are constructed for the stability of switched nonlinear time-delay systems with case (i). Then, the stability of the systems with case (ii) are explored. The contributions of the paper lie in that the stability with case (ii) is more general than existing results with case (i) and all switching laws considered are average dwell time switching that is less conservative than others switchings in literature. Finally, one example is provided to verify the effectiveness of the results.