Abstract :
Using the realization theoretic approach in [1-2] expressions are obtained for approximate solutions of Bezout type equations QX + RY = ??, together with the suprenum norm of the error. These are in terms of realizations as well as the Hankel maps associated with the given system. In the case of a commonly used algebra for infinite dimensional systems introduced by Collier and Desoer ([3-4],[8],[11]), our techniques in [1,2] and here become finite dimensional system theory techniques as developed in [6]. It is shown how, in that case, one can parameterize all approximating polynomial sequences for supremum norm approximation in the closed unit disc, thereby obtaining a systematic computational technique for finite dimensional stabilizing compensators. In particular, this paper provides a technique for characterization of stabilizing compensators for robust stabilization of a class of infinite dimensional systems by infinite and (quasi-)finite dimensional compensators for which realization techniques are known (Section 3). This is a much wider class of systems than typically considered ([3-4],[8],[11]). This includes a class of systems with transfer matrices in Nevalinna class (H??/H??), but not in L?? (see Section 4). A parametrization of the type of compensators introduced here is also given for robust stabilization and sensitivity problems.
