Abstract

This paper mainly addresses input-to-state stability (ISS) of nonautonomous nonlinear systems with infinite delays. We provide a novel definition for ISS of infinite-delayed systems, which can be seen as an extension of the existing ISS definition. A Lyapunov Krasovskii functional is proposed for verifying ISS of infinite-delayed systems. Applying the ISS Lyapunov functional method, a link between ISS of an infinite-delayed system and the exponential stability of its corresponding zero-input system is established. It is shown that a nonlinear system with infinite delays is ISS if its corresponding zero-input system is globally exponentially stable, provided that some Lipschitz and/or Lipschitz-like conditions are satisfied. Two illustrative examples are provided to show the effectiveness of our results.

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