The Unified Algebraic Characteristics on Stabilizing Feedback Controllers of Discrete-time Linear Systems

In this paper, according to the generalized inverse theory, we give the algebraic structures of stabilizing feedback controllers to discrete-time linear systems. Necessary and sufficient conditions for stability of the systems are given. A class of stable state feedback controller is designed. Stabilizing analysis for the discrete-time linear system provides a theoretical guidance to the new method, and explains this method in practical engineering control system design possibility. As an application, a new result for stochastic constant system is given. The paper gives the corresponding numerical example.