Stability analysis of Lur’e systems with a pulse-modulated feedback

Abstract

A nonlinear system with a sector bound nonlinearity is considered. The system is subject to a stabilizing sampled feedback with finite width impulses. An impulsive counterpart of the circle criterion for absolute stability is obtained with the help of the Gelig’s averaging method.

Gelig’s Averaging Method For Local Stabilization Of A Class Of Nonlinear Systems By A Pulse-Width Modulated Control

“…For brevity we will use notation t n = nT . Our analysis will be based on the Gelig's version of the averaging method [Gelig, 1982;Gelig and Churilov, 1998] and some additional mathematical technique from [Churilov, 2018;Churilov, 2019a;Churilov, 2019c]. The square of the nth pulse (taking the sign into account) can be calculated by the formula…”

“…In our recent research (37) was taken as a benchmark system for different schemes of stabilization. In [Churilov, 2019a] a system with a nonuniform sampling and a bounded duty ratio was analyzed. A sawtooth stabilizing signal was considered in [Churilov, 2019b].…”

Optimal interface controller design for haptic system

“…The spring damper interface circuitry C(s) is implemented as haptic interface controller [Eom et al, 2000] as given in (2). Zero Order Hold (ZOH) and quantization are the part of conversion and stability [Churilov, 2019].…”

“…Several authors have proposed various method for stability analysis. Authors have proposed stability using Lyapunov like function [Churilov, 2019], and Lyapunov function with parametric effect [Andreev, 2019]. Moreover, an adaptive algorithm for restoring mixed noise has been proposed by Thang et al [Thang et al, 2019].…”