Current‐estimation‐based iterative algorithms for solving periodic Lyapunov matrix equations

Abstract

In this study, two novel iterative algorithms are presented to solve the Lyapunov matrix equations appearing in discrete-time periodic linear systems. In both algorithms, a weighted combination of the estimation in the last and the current steps is used to update the estimation of the unknown matrices. It is shown that the sequences generated by the proposed algorithms with zero initial conditions monotonically converge to the unique positive definite solution of the periodic Lyapunov matrix equation if the associated system is asymptotically stable. Finally, a numerical example is used to illustrate the effectiveness of the proposed algorithms.