Conditions for QSR-dissipativity of the interconnection of hybrid systems with the sum of storage functions

This note explores the QSR-dissipativity of a class of hybrid dynamical systems. We first revisit and extend some existing definitions of dissipativity for hybrid systems. Subsequently, we explore some results regarding the relations between the QSR-dissipativity property of one open hybrid subsystem and its stability. Next, we shift focus to studying the negativefeedback interconnection of two hybrid subsystems, deriving new results about the existence of storage functions guaranteeing that the interconnection between two individual QSR-dissipative hybrid subsystems remains QSR-dissipative in the presence of external input signals. Analyzing such interconnections of hybrid systems may be intricate due to the possibility of both synchronous and asynchronous jumps occurring among the two subsystems, as previously acknowledged by the existing literature.