A Transfer-Function Approach to Linear Time-Varying Discrete-Time Systems

Abstract

In the first part of the paper a transfer-function approach is developed for the class of linear time-varying discrete-time systems. The theory is specified in terms of skew (noncommutative) rings of polynomials and formal power series, both with coefficients in a ring of time functions. The transfer-function matrix is defined to be a matrix whose entries belong to a skew ring of formal power series. It is shown that various system properties, such as asymptotic stability, can be characterized in terms of the skew-ring framework. In the last part of the paper, the transfer-function framework is applied to the study of feedback control. New results are obtained on assignability of system dynamics by using dynamic output feedback and dynamic state feedback. The results are applied to the control of an armature-controlled do motor with a variable loading.