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Implicit iterative algorithms with a tuning parameter for discrete stochastic Lyapunov matrix equations

Implicit iterative algorithms with a tuning parameter for discrete stochastic Lyapunov matrix equations

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An implicit iterative algorithm is established for solving a class of Lyapunov matrix equations appearing in the discrete-time stochastic systems with multiplicative noise. This algorithm contains a tuning parameter which can be appropriately chosen such that it has better convergence performance. Some convergence conditions have been derived for the proposed iterative algorithm, and for a special case an approach is given to choose the optimal tuning parameter such that the algorithm has the best convergence performance. In addition, the properties of boundedness and monotonicity of the proposed algorithm are also investigated when the corresponding stochastic system is asymptotically mean-square stable.

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