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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 ei- ther (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 posi- tivity 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.

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