Dissipativity Theory for Singular Systems. Part I: Continuous-Time Case

In this paper we develop dissipativity results for continual nonlinear and linear singular systems. To the best knowledge of author results are nonexistent. We generalize dissipativity theory to nonlinear continuous 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 continuous-time system dynamics. Furthermore, extended Kalman-Yakubovich-Popov conditions in terms of the singular system dynamics characterizing dissipativeness via system storage functions are derived. Finally, the framework is specialized to passive and nonexpansive singular systems to provide a generalization of the classical notions of passivity and nonexpansivity for nonlinear singular systems.