Abstract
In this paper, a novel implicit iterative algorithm with some tuning parameters for solving the continuous-time generalized Lyapunov matrix equation is presented. The idea is from [1] in which an efficient iterative algorithm was presented to solve the coupled Lyapunov matrix equations for Markovian jump linear systems. By using the information in the current step and the previous steps, we introduce some tuning parameters in the Lyapunov implicit iterative algorithm to obtain the solution of the continuous-time generalized Lyapunov matrix equation. The convergence rate of the proposed algorithm can be significantly improved by appropriately choosing these tuning parameters. It is shown that the sequence generated by the present algorithm can converges to the solution of the generalized Lyapunov matrix equation. An example is given at the end of this paper to compare the efficiency and accuracy of the proposed algorithm with other exist methods in the literature.
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