Convergence to periodic regimes in nonlinear feedback systems with a strongly convex backlash

TL;DR

This paper analyzes nonlinear feedback systems with backlash modeled by strongly convex sets, providing estimates for Lyapunov exponents that describe how trajectories converge to periodic regimes under periodic inputs.

Contribution

It introduces new convergence estimates for nonlinear systems with strongly convex backlash, extending dissipation inequalities to differential inclusions.

Findings

Lyapunov exponents quantify convergence rates.

Trajectories converge to periodic regimes under periodic inputs.

Enhanced dissipation inequalities are developed for strongly convex sets.

Abstract

This paper considers a class of nonlinear systems consisting of a linear part with an external input and a nonlinear feedback with a backlash. Assuming that the latter is specified by a strongly convex set, we establish estimates for the Lyapunov exponents which quantify the rate of convergence of the system trajectories to a forced periodic regime when the input is a periodic function of time. These results employ enhanced dissipation inequalities for differential inclusions with strongly convex sets, which were used previously for the Moreau sweeping process.