Multi‐parametric iterative algorithms for discrete periodic Lyapunov matrix equations
Ai‐Guo Wu, Wenxue Zhang, Ying Zhang · IET Control Theory and Applications · 2019
Two multi‐parametric iterative algorithms are developed to solve the forward discrete periodic Lyapunov matrix equation associated with discrete‐time linear periodic systems. An important feature of one of the proposed algorithms is that the information in the current and the last steps is used to update the iterative sequence. Necessary and sufficient conditions for these two algorithms to be convergent are provided in terms of the roots of a set of polynomial equations. Based on these conditions, a two‐dimensional section method is established to search suboptimal tuning parameters for these two algorithms. In addition, convergence properties are also analysed for some special cases of the obtained algorithms. Finally, numerical examples are provided to illustrate the effectiveness of the proposed algorithms. It can be found that the presented algorithms have better convergence performance than some existing iterative algorithms by choosing proper tuning parameters.