Decomposable Dissipativity and Related Stability for Discrete-Time Switched Systems

This note investigates dissipativity and related stability for discrete-time switched systems. The new concept of decomposable dissipativity is proposed for this kind of systems. By decomposing the supply rate into the main supply rate and the subsidiary supply rate, the “energy” changes of subsystems and “energy” dissipation in the whole switched system are explained. The uniform stability conditions are derived for decomposable dissipative discrete-time switched systems. By the decomposition of supply rate, the non-positive condition of the supply rate, which is often required in the literature to derive stability, is relaxed. Finally, one example is given to illustrate the results.