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This paper proposes definitions of decomposable dissipativity and decomposable passivity for a class of hybrid systems to investigate stability properties and dissipativity-based control of this kind of hybrid system. Decomposable dissipativity is established via employing multiple flow-storage functions, jump-storage functions, flow-supply rates and jump-supply rates, which allows each subsystem to have its own storage function and supply rate. The decomposable dissipativity reveals the energy changes of activated and inactivated subsystems. Based on the proposed definitions, sufficient conditions of guaranteeing the stability of hybrid systems are derived, which relax the constraint on non-positive supply rates. Then, dissipativity- and passivity-based controllers are designed. In order to demonstrate the usefulness and effectiveness of the obtained results, two examples are provided.

Decomposable dissipativity and stability analysis of hybrid systems