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This paper considers the optimal time-weighted H2 model reduction problem for discrete Markovian jump linear systems (MJLSs). The purpose is to ¿nd a mean square stable MJLS of lower order such that the time-weighted H2 norm of the corresponding error system is minimized for a given mean square stable discrete MJLS. A new notation named time-weighted H2 norm of discrete MJLS is de¿ned for the model reduction purpose for the ¿rst time. Then a computational formula of the time-weighted H2 norm is given. Based on this formula, a gradient Àow method is proposed to solve the optimal time-weighted H2 model reduction problem. Finally, a numerical example is used to illustrate the effectiveness of the proposed approach.

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This paper is concerned with the problem of robust H ∞ control for uncertain stochastic systems with Markovian jump parameters and time-varying state delays. A linear matrix inequality approach is developed and state feedback controllers are designed, which guarantee mean square asymptotic stability of the closed-loop system and a prescribed H ∞ performance level for all modes and admissible uncertainties. A numerical example is provided to demonstrate the application of the proposed method.

No abstract