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

Logemann, Hartmut; Ryan, Eugene P.; Shvartsman, Ilya

ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 3, pp. 458-483.

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 $L^2$-stable, time-invariant linear system and a non-decreasing globally Lipschitz static output nonlinearity, or (b) an $L^2$-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.

Classification : 34G20, 47J40, 47N70, 93C23, 93C25, 93D10, 93D25
Mots clés : actuator nonlinearities, hysteresis, infinite-dimensional systems, input-output analysis, integral control, sensor nonlinearities

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