Time-optimal output regulators for linear multivariate discrete-time systems Part 2. All classes of right-invertible systems

Abstract

In Part 1 of this paper (Hassan and Amin 1987) a simple algebraic solution for the time-optimal output regulator problem was presented. This solution, which consists of a state feedback control law, has been obtained for all classes of right-invertible decouplable systems S(A, B, C, E). The results of Part 1 are here extended to all classes of right-invertible systems S(A, B, C, E). A set of optimal output deadbeat indices (called the ‘optimal set’) is defined and related to the observability indices of the optimal closed-loop system. The time-optimal output regulator problem for a right-invertible non-decouplable system S(A, B, C, E) is resolved by transforming S into a decouplable system Sc(A, B, Cc, Ec) having the optimal output deadbeat index σ* of S. First, an algorithm is presented to construct iteratively, in a well-defined optimal sense, a unimodular left compensator L(z) and a compensated decouplable system Sc(A, B, Cc, Ec) from the state-space parameters of S. Then, a family of optimal state fee...