Self-Excited Dynamics of Discrete-Time Lur'e Models with Affinely Constrained, Piecewise-C1 Feedback Nonlinearities

TL;DR

This paper investigates the conditions under which discrete-time Lur'e models with specific nonlinearities exhibit self-excited behavior, characterized by bounded yet nonconvergent responses for most initial conditions.

Contribution

It provides new sufficient conditions ensuring boundedness and nonconvergence in discrete-time Lur'e models with affinely constrained, piecewise-C1 nonlinearities.

Findings

Bounded responses for all initial conditions

Nonconvergent behavior for almost all initial conditions

Sufficient conditions for self-excitation in the models

Abstract

Self-excited systems (SES) arise in numerous applications, such as fluid-structure interaction, combustion, and biochemical systems. In support of system identification and digital control of SES, this paper analyzes discrete-time Lur'e models with affinely constrained, piecewise-C1 feedback nonlinearities. The main result provides sufficient conditions under which a discrete-time Lur'e model is self-excited in the sense that its response is 1) bounded for all initial conditions, and 2) nonconvergent for almost all initial conditions.