Self-Excited Dynamics of Discrete-Time Lur'e Systems

TL;DR

This paper investigates the conditions under which discrete-time Lur'e systems with saturation nonlinearities exhibit self-excited behavior, characterized by bounded yet nonconvergent responses, relevant to various scientific applications.

Contribution

It provides new sufficient conditions for self-excitation in discrete-time Lur'e systems with saturation nonlinearities, advancing understanding of their dynamic behavior.

Findings

Identifies conditions for bounded, nonconvergent responses

Analyzes the impact of piecewise-linear saturation nonlinearities

Extends theory to discrete-time systems with practical nonlinearities

Abstract

Self-excited systems arise in numerous applications, such as biochemical systems, fluid-structure interaction, and combustion. This paper analyzes a discrete-time Lur'e system with a piecewise-linear saturation feedback nonlinearity. The main result provides sufficient conditions under which the Lur'e system is self-excited in the sense that its response is bounded and nonconvergent.