Lyapunov characterization of input-to-state stability for semilinear control systems over Banach spaces

Andrii Mironchenko; Fabian Wirth

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arXiv · 1708.07953

Lyapunov characterization of input-to-state stability for semilinear control systems over Banach spaces

Andrii Mironchenko·Fabian Wirth

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Abstract

We prove that input-to-state stability (ISS) of nonlinear systems over Banach spaces is equivalent to existence of a coercive Lipschitz continuous ISS Lyapunov function for this system. For linear infinite-dimensional systems, we show that ISS is equivalent to existence of a non-coercive ISS Lyapunov function and provide two simpler constructions of coercive and non-coercive ISS Lyapunov functions for input-to-state stable linear systems.

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Andrii Mironchenko, Fabian Wirth. 2017-08-26. Lyapunov characterization of input-to-state stability for semilinear control systems over Banach spaces. https://arxiv.org/abs/1708.07953

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