Gradient Based Iterative Algorithm to Solve General Coupled Discrete-Time Periodic Matrix Equations over Generalized Reflexive Matrices

Abstract

The discrete-time periodic matrix equations are encountered in periodic state feedback problems and model reduction of periodic descriptor systems. The aim of this paper is to compute the generalized reflexive solutions of the general coupled discrete-time periodic matrix equations. We introduce a gradient-based iterative (GI) algorithm for finding the generalized reflexive solutions of the general coupled discretetime periodic matrix equations. It is shown that the introduced GI algorithm always converges to the generalized reflexive solutions for any initial generalized reflexive matrices. Finally, two numerical examples are investigated to confirm the efficiency of GI algorithm.