On ISS-Lyapunov functions for infinite-dimensional linear control systems subject to saturations

TL;DR

This paper develops ISS-Lyapunov functions for infinite-dimensional linear control systems under saturation effects, providing explicit functions in some cases and existence results in others.

Contribution

It introduces methods to derive ISS-Lyapunov functions for infinite-dimensional systems with saturations, covering cases where saturation acts in the same or different spaces.

Findings

Explicit ISS-Lyapunov functions for saturation in the control space

Existence of ISS-Lyapunov functions when saturation acts in a different space

Applicable to infinite-dimensional linear control systems

Abstract

- This article deals with the derivation of ISS-Lyapunov functions for infinite-dimensional linear systems subject to saturations. Two cases are considered: 1) the saturation acts in the same space as the control space; 2) the saturation acts in another space, especially a Banach space. For the first case, an explicit ISS-Lyapunov function can be derived. For the second case, we can only ensure the existence of an ISS-Lyapunov function.