Accelerated smith iterative algorithms for coupled Lyapunov matrix equations

In this paper, a kind of explicit iterative algorithm is studied by using Smith methods for solving coupled Lyapunov matrix equations arising in continuous-time Markovian jump linear systems. First, by introducing the latest estimation, a current-estimation-based Smith iterative algorithm is presented to solve the considered matrix equations. The monotonicity and boundedness of the sequence generated by this algorithm with zero initial conditions are shown by the mathematical induction, and a convergence result is accordingly obtained based on these two properties. To further improve the convergence performance, an accelerated Smith iterative algorithm is proposed. Convergence analysis indicates the iterative solutions generated by the developed algorithms always converge to the unique solutions of the coupled Lyapunov matrix equations for any initial conditions. A numerical example is provided to show the effectiveness of the presented iterative algorithms.