Low-Gain Integral Control of Well-Posed Linear Infinite-Dimensional Systems with Input and Output Nonlinearities
✍ Scribed by T. Fliegner; H. Logemann; E.P. Ryan
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 224 KB
- Volume
- 261
- Category
- Article
- ISSN
- 0022-247X
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✦ Synopsis
Time-varying low-gain integral control strategies are presented for asymptotic tracking of constant reference signals in the context of exponentially stable, wellposed, 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 → 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.