THE OPTIMAL PROJECTION EQUATIONS FOR FINITE-DIMENSIONAL FIXED-ORDER H-2-OPTIMAL CONTROL OF INFINITE-DIMENSIONAL DISCRETE-TIME-SYSTEMS

In this paper we are concerned with the fixed, finite-order H-2-optima l control of linear, infinite-dimensional discrete-time systems. The s et of necessary conditions for the existence of the H-2-optimal contro ller is expressed in terms of four operator equations (two modified Ri ccati equations and two modified Lyapunov equations) coupled by a proj ector having the rank given by the dimension of the compensator state. It is shown that, when the order of the compensator is equal to the o rder of the plant, the four operator equations are decoupled and we ob tain the infinite-dimensional generalization of the finite-dimensional state-space solution to the H-2-optimal control problem for time-vary ing systems, as given by Ionescu and Weiss (1992).