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 studies the problem of state estimator design for stochastic twodimensional (2D) discrete systems described by the secondary 2D Fornasini-Marchesini odel subject to white noise in both the state and measurement equations. The aim is to design a 2D Kalman filter that minimizes the variance of the estimation error of the state vectors. An explicit formulation of the estimator is derived, based on which, an algorithm for the design of the desired Kalman filter is proposed. Finally, examples are provided to demonstrate the effectiveness of the proposed method.

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