Sufficient conditions for passivity and stability of interconnections of hybrid systems using sums of storage functions

Abstract

Building from recent results on passivity for a class of hybrid systems, we investigate the properties of negative feedback interconnections of such systems. We establish links between the passivity properties of the individual subsystems and passivity, stability, and asymptotic stability of their interconnection. As a main difference to the continuous time counterpart, it is found that the sum of the two storage functions of two individual hybrid subsystems may not be a storage function for their interconnection. This issue motivates exploring additional sufficient conditions that guarantee that passivity and stability of the interconnected system hold using the individual storage functions. Throughout the paper, an application and examples illustrate the definitions and the results obtained.