LOW-GAIN CONTROL OF UNCERTAIN REGULAR LINEAR-SYSTEMS

It is well known that closing the loop around an exponentially stable, finite-dimensional, Linear, time-invariant plant with square transfer -function matrix G(s) compensated by a controller of the form (k/s)Gam ma(0), where k is an element of R and Gamma(0) is an element of R(mxm) , will result in an exponentially stable closed-loop system which achi eves tracking of arbitrary constant reference signals, provided that ( i) all the eigenvalues of G(0)Gamma(0) have positive real parts and (i i) the gain parameter k is positive and sufficiently small. In this pa per we consider a rather general class of infinite-dimensional 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 o f exponentially stable regular systems and (ii) we show how the parame ters k and Gamma(0) can be tuned adaptively. The resulting adaptive tr acking controllers are not based on system identification or parameter estimation algorithms, nor is the injection of probing signals requir ed.