Reflexive periodic solutions of general periodic matrix equations

Abstract

Analysis and design of linear periodic control systems are closely related to the periodic matrix equations. The objective of this paper is to provide four new iterative methods based on the conjugate gradient normal equation error (CGNE), conjugate gradient normal equation residual (CGNR), and least‐squares QR factorization (LSQR) algorithms to find the reflexive periodic solutions (X1,Y1,X2,Y2,…,Xσ,Yσ) of the general periodic matrix equations ∑s=0σ−1Ai,sXi+sBi,s+∑t=0σ−1Ci,tYi+tDi,t=Ni, for i = 1,2,…,σ. The iterative methods are guaranteed to converge in a finite number of steps in the absence of round‐off errors. Finally, some numerical results are performed to illustrate the efficiency and feasibility of new methods.

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