𝔖 Bobbio Scriptorium
✦   LIBER   ✦

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

No coin nor oath required. For personal study only.

✦ 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.