A REALIZATION-THEORY FOR PERTURBED LINEAR-SYSTEMS

In this paper we present a theory which characterizes LTI state-space realizations of perturbed rational transfer function matrices. Our app roach is to model system perturbations as sequences in the space of ra tional matrices. First, we give a definition of convergence in the spa ce of rational matrices which is motivated by the kinds of parameter u ncertainties occurring in many robust control problems. A realization theory is then established under the constraint that the realization o f any convergent sequence of rational matrices should also be converge nt. Next, we consider the issue of minimality of realizations and prop ose a method for calculating the dimension of a minimal realization of a given transfer matrix sequence. Finally, necessary and sufficient c onditions are discussed under which a sequence of state-space systems is a minimal realization and under which minimal realizations of the s ame transfer function sequence are state-space equivalent. Relationshi ps with standard algebraic system theoretic results are discussed. (C) 1994 Academic Press, Inc.