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Low-gain integral control of well-posed linear infinite-dimensional systems with input and output nonlinearities. (English) Zbl 0993.93017

Authors’ abstract: Time-varying low-gain integral control strategies are presented for asymptotic tracking of constant reference signals in the context of exponentially stable, well-posed, linear, infinite-dimensional, single-input-single-output systems – subject to globally Lipschitz, nondecreasing input and output nonlinearities. It is shown that applying error feedback using an integral controller ensures that the tracking error is small in a certain sense, provided that (a) the steady-state gain of the linear part of the system is positive, (b) the reference value \(r\) is feasible in an entirely natural sense, and (c) the positive gain function \(t\mapsto k(t)\) is ultimately sufficiently small and not of class \(L^1\). Under a weak restriction on the initial data it is shown that (a), (b), and (c) ensure asymptotic tracking. If, additionally, the impulse response of the linear part of the system is a finite signed Borel measure, the global Lipschitz assumption on the output nonlinearity may be considerably relaxed.

MSC:

93C25 Control/observation systems in abstract spaces
03C10 Quantifier elimination, model completeness, and related topics
93C40 Adaptive control/observation systems
93B51 Design techniques (robust design, computer-aided design, etc.)
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References:

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