Input-to-state stability meets small-gain theory

Andrii Mironchenko

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arXiv · 2406.17909

Input-to-state stability meets small-gain theory

Andrii Mironchenko

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Abstract

Input-to-state stability (ISS) unifies global asymptotic stability with respect to variations of initial conditions with robustness with respect to external disturbances. First, we present Lyapunov characterizations for input-to-state stability as well as ISS superpositions theorems showing relations of ISS to other robust stability properties. Next, we present one of the characteristic applications of the ISS framework - the design of event-based control schemes for the stabilization of nonlinear systems. In the second half of the paper, we focus on small-gain theorems for stability analysis of finite and infinite networks with input-to-state stable components. First, we present a classical small-gain theorem in terms of trajectories for the feedback interconnection of 2 nonlinear systems. Finally, a recent Lyapunov-based small-gain result for a network with infinitely many ISS components is shown.

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Andrii Mironchenko. 2024-06-25. Input-to-state stability meets small-gain theory. https://arxiv.org/abs/2406.17909

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