Extended Kalman-Yakubovich-Popov conditions for singularly impulsive dynamical systems

Singularly impulsive (or generalized impulsive) dynamical systems are systems which dynamics are characterized by the set of differential, difference and algebraic equations. They represent the class of hybrid systems, where algebraic equations represent constraints that differential and difference equations need to satisfy. For the class of singularly impulsive dynamical systems we present extended Kalman-Yakubovich-Popov conditions in terms of the singularly impulsive system dynamics characterizing dissipativeness via system storage functions. The framework is specialized to passive and nonexpansive singularly impulsive systems to provide a generalization of the classical notions of passivity and nonexpansivity for nonlinear singularly impulsive systems.