Poles, zeros, and feedback: State space interpretation

Abstract

This paper is concerned with the relationships between time and frequency domain descriptions of linear, time-invariant systems and with the evaluation of the effects of feedback on such systems. A new expression for the transfer function of a system described by a set of first-order differential equations is given; this expression not only relates the poles and zeros to the eigenvalues of matrices but also makes it possible to compute the transfer function without matrix inversion. The effects of state variable feedback on controllability, observability, and pole-zero configurations are discussed and the effects of feeding back the output and its derivatives are considered. The application of these ideas to an optimal control problem is sketched and methods of extending them to the multi-input, multi-output case are examined.