Stability Analysis of Discrete-time Lure Systems with Slope-restricted Odd Monotonic Nonlinearities

TL;DR

This paper presents less conservative stability conditions for discrete-time Lure systems with slope-restricted odd nonlinearities, using a novel Lyapunov function and LMIs, improving analysis accuracy in real applications.

Contribution

It introduces a new Lyapunov function and LMI-based criteria for stability analysis of Lure systems with slope-restricted odd nonlinearities, reducing conservatism compared to existing methods.

Findings

Derived less conservative stability criteria using LMIs.

Numerical examples show significant reduction in conservatism.

Applicable to real-world systems with slope-restricted odd nonlinearities.

Abstract

Many nonlinear dynamical systems can be written as Lure systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global asymptotic stability analysis of discrete-time Lure systems in which the nonlinearities have restricted slope and/or are odd, which is the usual case in real applications. A Lure-Postnikov-type Lyapunov function is proposed that is used to derive sufficient analysis conditions in terms of linear matrix inequalities (LMIs). The derived stability critera are provably less conservative than criteria published in the literature, with numerical examples indicating that conservatism can be reduced by orders of magnitude.