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Finite Horizon H_{2}/H_{\infty } Control for Discrete-Time Stochastic Systems With Markovian Jumps and Multiplicative Noise

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3 Author(s)
Ting Hou ; Coll. of Inf. & Electr. Eng., Shandong Univ. of Sci. & Technol., Qingdao, China ; Weihai Zhang ; Hongji Ma

In this note, we consider the finite horizon mixed H 2/H control problem for discrete-time stochastic linear systems subject to Markov jump parameters and multiplicative noise. Firstly, we derive a stochastic bounded real lemma (SBRL), which is used to establish a necessary and sufficient condition for the existence of the mixed H 2/H control via the solvability of four coupled difference matrix-valued recursions (CDMRs). Moreover, a state feedback H 2/H controller is designed by means of the solutions of CDMRs.

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Automatic Control, IEEE Transactions on  (Volume:55 ,  Issue: 5 )