On the Control of Linear Multiple Input-Output Systems*

The control of linear time-invariant systems is one of the most basic problems of modern automatic control theory. Although “optimal controllers” which minimize certain costs associated with control can be determined, in most applications “simple controllers” suffice, and are often more desirable. The criteria by which these simple controllers are designed are closely related to the problem of assigning the eigenvalues of the fundamental matrix (i.e., the poles of the system) to arbitrary but specified locations. This paper presents an approach to the design of such control systems. Our approach does not involve computing complicated canonical forms, as do some previous methods, and at the same time generalizes easily to multi-input-output systems. A simple solution of the problem of designing feedback control systems with a minimum number of dynamic elements is also presented.