Dissipativity theory for singular systems. Part II: Discrete-time case

In this paper we develop dissipativity results for discrete nonlinear and linear singular systems. To the best knowledge of author results are nonexistent. We generalize dissipativity theory to discrete nonlinear singular dynamical systems. Specifically, the classical concepts of system storage functions and supply rates are extended to singular dynamical systems providing a generalized system energy interpretation in terms of stored energy and dissipated energy over the discrete-time system dynamics. For the class of discrete singular systems we present Kalman-Yakubovich-Popov conditions in terms of the discrete singular system dynamics characterizing dissipativeness via system storage function. The framework is specialized to passive and nonexpansive discrete singular systems to provide a generalization of the classical notions of passivity and nonexpansivity for nonlinear discrete singular systems.