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This paper investigates the linear minimum mean square error state estimation for discrete-time systems with Markov jump delays.In order to solve the optimal estimation problem,the single Markov delayed measurement is rewritten as an equivalent measurement with multiple constant delays,then a delay-free Markov jump linear system is obtained via state augmentation.The estimator is derived on the basis of the geometric arguments in the Hilbert space,and a recursive equation of the filter is obtained by solving the Riccati equations.It is shown that the proposed state estimator is exponentially stable under standard assumptions.
This paper investigates the linear minimum mean square error state estimation for discrete-time systems with Markov jump delays. In order to solve the optimal estimation problem, the single Markov delayed measurement is rewritten as an equivalent measurement with multiple constant delays, then a delay- free Markov jump linear system is derived via state augmentation. The estimator is derived on the basis of the geometric arguments in the Hilbert space, and a recursive equation of the filter is obtained by solving the Riccati equations. It is shown that the proposed state estimator is exponentially stable under standard assumptions.