Stability Analysis and Controller Design for a Linear System with Duhem Hysteresis Nonlinearity

TL;DR

This paper analyzes the stability of linear systems interconnected with Duhem hysteresis nonlinearities, providing conditions for stability based on input-output properties and a control design method that does not need detailed hysteresis models.

Contribution

It introduces a novel stability analysis framework and a control design methodology for linear systems with hysteresis, relying on CCW/CW properties without precise hysteresis modeling.

Findings

Derived sufficient stability conditions based on CCW/CW properties.

Developed a control design method for hysteretic actuators or sensors.

Validated the approach through theoretical analysis and simulations.

Abstract

In this paper, we investigate the stability of a feedback interconnection between a linear system and a Duhem hysteresis operator, where the linear system and the Duhem hysteresis operator satisfy either the counter-clockwise (CCW) or clockwise (CW) input-output dynamics. More precisely, we present sufficient conditions for the stability of the interconnected system that depend on the CW or CCW properties of the linear system and the Duhem operator. Based on these results we introduce a control design methodology for stabilizing a linear plant with a hysteretic actuator or sensor without requiring precise information on the hysteresis operator.