Passivity Analysis of Nonlinear Impulsive Multi-Dimensional Switched Systems

In this paper, we extend the classic passivity theory for a class of nonlinear impulsive multi-dimensional switched systems with both (exponentially) passive and nonpassive subsystems, where the state changes (i.e., state dimensional variations and/or state jumps) may occur at the switching moments. The passivity conditions of such systems are studied by adopting the transition-dependent average dwell time (TDADT) and multiple Lyapunov functions (MLFs). The state changes of such systems are taken into account by introducing the switching time threshold and the switching rate conditions. The proposed methods prove that, with a relaxed quasi-alternative switching signal, nonlinear impulsive multi-dimensional switched systems with both exponentially passive and nonpassive subsystems are (weakly) exponentially passive, and systems with both passive and nonpassive subsystems are (weakly) passive. The main results are demonstrated by a numerical example.