ISS-Lyapunov functions for discontinuous discrete-time systems

Titelangaben

Grüne, Lars ; Kellett, Christopher M.:
ISS-Lyapunov functions for discontinuous discrete-time systems.
In: IEEE Transactions on Automatic Control. Bd. 59 (2014) Heft 11 . - S. 3098-3103.
ISSN 1558-2523
DOI: https://doi.org/10.1109/TAC.2014.2321667

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Abstract

Input-to-State Stability (ISS) and the ISS-Lyapunov function are useful tools for the analysis and design of nonlinear systems. 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 ISS-Lyapunov functions for discrete-time systems with discontinuous dynamics.