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; firstname.lastname@example.org; email@example.com; firstname.lastname@example.org
Revised: 20 March 2006
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.
Mathematics Subject Classification: 34G20 / 47J40 / 47N70 / 93C23 / 93C25 / 93D10 / 93D25
Key words: Actuator nonlinearities / hysteresis / infinite-dimensional systems / input-output analysis / integral control / sensor nonlinearities
© EDP Sciences, SMAI, 2007