Stability of interconnected switched systems using QSR dissipativity with multiple supply rates

This paper considers a notion of QSR dissipativity for discrete-time switched systems that uses multiple supply rates. The focus on switched systems is motivated by cyber physical systems (CPS) where physical dynamics interact with discrete-event or logical dynamics. The notion of QSR dissipativity used in this paper is based on previous work on QSR dissipativity for non-switched systems and decomposable dissipativity for switched systems. The notion of QSR dissipativity is well established for non-switched systems and generalizes many system results including both the passivity theorem and the small gain theorem. In decomposable dissipativity, separate supply rates are developed for each subsystem depending on whether it is currently active or inactive. This paper presents this definition of QSR dissipativity for switched systems and then uses it to prove stability for single systems and interconnected systems. Beyond stability, the dissipative property for interconnected systems is shown. This allows for large scale systems to be studied using successive dissipative assessments. When considering passive systems, these results are studied in more detail.