On the design of linear time invariant systems by periodic output feedback Part I. Discrete-time pole assignment†

Abstract

In this paper it is shown that complete controllability and complete observability are necessary and sufficient conditions for discrete-time pole assignment by output feedback for linear time-invariant systems. The resultant output feedback gain is a periodic function of time with a period equal to the sampling interval. It is also shown that periodic discrete-output feedback gains can be used in stabilizing a linear time-invariant system if and only if its unstable modes are controllable and observable.