Generalized passivity in discrete-time switched nonlinear systems

This paper analyzes the passivity and feedback passivation problems for discrete-time switched nonlinear systems with both passive and nonpassive modes that have relative degree zero. We generalize the classical passivity definition for such a switched nonlinear system provided that the increase in storage function over a finite horizon is bounded by the total supplied energy during this time period. We further extend this generalized passivity definition to switched nonlinear systems with passive, feedback passive modes and modes which can not be rendered passive using feedback (non-feedback passive modes). The switched nonlinear system is proved to be locally feedback passive if and only if its zero dynamics are locally passive. A lower bound on the ratio of total activation time between (feedback) passive and non-feedback passive modes is obtained to guarantee passive zero dynamics with Lipschitz constraints. We prove that output feedback control can be used to stabilize the equilibrium point of the switched system.