On Lyapunov Methods for Nonlinear Discrete-Time Switching Systems With Dwell-Time Ranges

A novel Lyapunov methodology for the stability check of nonlinear discrete-time switching systems, equipped with switches digraphs and nonuniform dwell-time ranges, is here presented. The novelty of the methodology consists in the following coexisting features: i) the global uniform (with respect to compact sets of initial conditions and switching signals) asymptotic stability is addressed; ii) the information on allowed switches and (nonuniform) dwell-time ranges is fully exploited; iii) no assumption is introduced on either stability or instability of the subsystems; iv) no assumption is introduced on the regularity of the functions describing the dynamics; v) the number of involved Lyapunov functions is always equal to the number of different modes; vi) a set of Lyapunov inequalities is uniquely defined coping with all scenarios of allowed switches and dwell-time ranges; vii) the provided Lyapunov conditions are necessary and sufficient for the global uniform asymptotic stability. Linear matrix inequalities obtained by this methodology are shown for the linear case.