ISS-Lyapunov Functions for Discontinuous Discrete-Time Systems

Abstract : Input-to-State Stability (ISS) and the ISS-Lyapunov function have proved to be useful tools for the analysis and design of nonlinear systems in a variety of contexts. Motivated by the fact that many feedback control laws, such as model predictive control or event-based control, lead to discontinuous discrete-time dynamics, we investigate ISS-Lyapunov functions for such systems. ISS-Lyapunov functions were originally introduced in a so-called implication form and, in many cases, this has been shown to be equivalent to an ISS-Lyapunov function of dissipative form. However, for discontinuous dynamics, we demonstrate via an example that this equivalence no longer holds. We therefore propose a stronger implication form ISS-Lyapunov function and provide a complete characterization of ISSLyapunov functions for discrete-time systems with discontinuous dynamics.
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IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2014, PP (99), 〈10.1109/TAC.2014.2321667〉
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Lars Grüne, Christopher M. Kellett. ISS-Lyapunov Functions for Discontinuous Discrete-Time Systems. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2014, PP (99), 〈10.1109/TAC.2014.2321667〉. 〈hal-00944360〉

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