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LowGain Control of Uncertain Regular Linear Systems
, 1994
"... It is wellknown that closing the loop around an exponentially stable, finitedimensional, linear, timeinvariant plant with square transferfunction matrix G(s) compensated by a controller of the form (k=s)\Gamma 0 , where k 2 Rand \Gamma 0 2 R m\Thetam , will result in an exponentially stable clos ..."
Abstract

Cited by 30 (19 self)
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It is wellknown that closing the loop around an exponentially stable, finitedimensional, linear, timeinvariant plant with square transferfunction matrix G(s) compensated by a controller of the form (k=s)\Gamma 0 , where k 2 Rand \Gamma 0 2 R m\Thetam , will result in an exponentially stable closedloop system which achieves tracking of arbitrary constant reference signals, provided that (i) all the eigenvalues of G(0)\Gamma 0 have positive real parts and (ii) the gain parameter k is positive and sufficiently small. In this paper we consider a rather general class of infinitedimensional linear systems, called regular systems, for which convenient representations are known to exist, both in time and in frequency domain. The purpose of the paper is twofold: (i) we extend the above result to the class of exponentially stable regular systems and (ii) we show how the parameters k and \Gamma 0 can be tuned adaptively. The resulting adaptive tracking controllers are not based on syst...