Finite-time stability properties of Lur'e systems with piecewise continuous nonlinearities

TL;DR

This paper investigates the finite-time stability of Lur'e systems with piecewise continuous nonlinearities using set-valued Lie derivatives, extending existing results and applying them to mechanical and neural network systems.

Contribution

It introduces new conditions for finite-time stability of Lur'e systems with piecewise nonlinearities, expanding the theoretical understanding and practical applicability.

Findings

Established global asymptotic stability under a general sector condition.

Derived conditions for output and state finite-time stability.

Validated results on mechanical systems with friction and cellular neural networks.

Abstract

We analyze the stability properties of Lur'e systems with piecewise continuous nonlinearities by exploiting the notion of set-valued Lie derivative for Lur'e-Postnikov Lyapunov functions. We first extend an existing result of the literature to establish the global asymptotic stability of the origin under a more general sector condition. We then present the main results of this work, namely additional conditions under which output and state finite-time stability properties also hold for the considered class of systems. We highlight the relevance of these results by certifying the stability properties of two engineering systems of known interest: mechanical systems affected by friction and cellular neural networks.