Time-optimal output regulators for linear multivariable discrete-time systems Part 1. Right invertible decouplable systems

Corsetti and Houpis (1985) presented a simple algebraic solution for the timeoptimal output regulator problem. This solution has been obtained for a special class of right invertible decouplable systems S(A, B, C) satisfying the condition that CB is of full rank. In this paper a general method is presented to extend the results of Corsetti and Houpis to all classes of right invertible decouplable systems S(A, B, C, E). It is shown that a simple state feedback control law drives each output of S(A, B, C, E) in a minimum number of steps equal to the order of the associated infinite zero. This state feedback represents the optimal solution for the considered time-optimal output regulator problem. A class of optimal solutions, parametrized by a free parameter matrix K, is obtained for non-square systems. The properties of the resulting optimal closed-loop system is given and a numerical example is worked out to illustrate the generality and feasibility of the proposed method.