On the Control of Linear Multiple Input-Output Systems

In recent years there has been a considerable amount of interest in the problem of designing controllers for linear systems. Although most of the theoretical interest has centered around optimal control approaches, it is generally known t h a t in most standard control systems, simple and usually nonoptimal controllers suffice. One of the oldest problems of control theory is that of stabilizing a linear control system by using feedback (see Fig. 1). Although this problem has been solved in the single input-output case by many people, one of the first clear statements was that by D. G. Luenberger. 1 In the case of multiple input-outputs, elegant solutions are of recent origin (see Ref. 2). Almost all of the published solutions resort to canonical forms, and in the multiple input-output case are not convenient to work * A talk based on this paper was presented at the Second Assilomar Conference on Circuits and System Theory, 1968. 1063 1064 T H E BELL SYSTEM TECHNICAI J O U R N A L , MARCH