ANALYSIS OF THE POLE-ZERO CANCELLATIONS IN A CLASS OF H infinity OPTIMAL CONTROL PROBLEMS.

Abstract

A study of the pole-zero cancellations which occur in a class of H infinity control problems which may be embedded in a given configuration is presented. The class is characterized by the assumption that both P//1 //2 (s) and P//2 //1 (s) are square but not necessarily of the same size. A general bound is desired on the McMillan degree of all controllers which are stabilizing and lead to a closed loop which satisfies parallel R(s) parallel infinity less than equivalent to p (p need not be optimal in the L infinity -norm sense). If the McMillan degree of P(s) given is n it is shown that in the single-loop (SISO) case the corresponding (unique) H infinity -optimal controller never requires more than n-1 states. In the multivariable case, there is a continuum of optimal controllers whose McMillan degree satisfies this same bound, although other controllers with higher McMillan degree exist.