Results on input-to-state stability for hybrid systems
Chaohong Cai; Teel, A.R.
Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC apos;05. 44th IEEE Conference on
Volume , Issue , 12-15 Dec. 2005 Page(s): 5403 - 5408
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Summary: We show that, like continuous-time systems, zero-input locally asymptotically stable hybrid systems are locally input-to-state-stable (LISS). We demonstrate by examples that, unlike continuous-time systems, zero-input locally exponentially stable hybrid systems may not be LISS with linear gain, input-to-state stable (ISS) hybrid systems may not admit any ISS Lyapunov function, and nonuniform ISS hybrid systems may not be (uniformly) ISS. We then provide a strengthened ISS condition as an equivalence to the existence of an ISS Lyapunov function for hybrid systems. This strengthened condition reduces to standard ISS for continuous-time and discrete-time systems. Finally under some other assumptions we establish the equivalence among ISS, several asymptotic characterizations of ISS, and the existence of an ISS Lyapunov function for hybrid systems.

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