3 / 2016-05-21 17:07:51

An Iterative Algorithm for Solving Periodic Lyapunov Equation

10152,10153,10154

Periodic Lyapunov matrix equation plays a very important role in analysis and design of periodic linear systems. In this paper, a novel implicit iterative algorithm with a tuning parameter is developed to solve the forward-time discrete-time periodic Lyapunov matrix equation associated with the discrete-time linear periodic system. A significant feature of the proposed algorithm is that the iterative sequences are updated by using not only the information in the last step, but also the information in the current step and the previous step. The convergence rate of the proposed algorithm can be significantly improved by choosing appropriate parameter in this algorithm. It is shown that the sequence generated by this algorithm with zero initial conditions monotonically converges to the unique positive definite solution of the periodic Lyapunov matrix equation. Some theoretical proofs for the convergence of the proposed algorithm are provided in this technical note. In addition, a method to choose the optimal parameter is given for this algorithm. Finally, three numerical examples are provided to illustrate the effectiveness of the algorithm.