Integral control of infinite-dimensional systems in the presence of hysteresis: an input-output approach

Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK; hl@maths.bath.ac.uk; epr@maths.bath.ac.uk; shvartia@muohio.edu

Received: 27 September 2005
Revised: 20 March 2006

Abstract

This paper is concerned with integral control of systems with hysteresis. Using an input-output approach, it is shown that application of integral control to the series interconnection of either (a) a hysteretic input nonlinearity, an L²-stable, time-invariant linear system and a non-decreasing globally Lipschitz static output nonlinearity, or (b) an L²-stable, time-invariant linear system and a hysteretic output nonlinearity, guarantees, under certain assumptions, tracking of constant reference signals, provided the positive integrator gain is smaller than a certain constant determined by a positivity condition in the frequency domain. The input-output results are applied in a general state-space setting wherein the linear component of the interconnection is a well-posed infinite-dimensional system.