Finite Horizon H/H Control for Discrete-Time Stochastic Systems With Markovian Jumps and Multiplicative Noise

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 condit...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 55; no. 5; pp. 1185 - 1191
Main Authors Ting Hou, Weihai Zhang, Hongji Ma
Format Journal Article
LanguageEnglish
Published IEEE 01.05.2010
Subjects
Control systems
Coupled difference matrix-valued recursions
discrete- time systems
H_{2}/H_{\infty} control
Infinite horizon
Investments
Linear feedback control systems
Linear systems
Markov jump
Nonlinear control systems
Portfolios
Stochastic resonance
Stochastic systems
Sufficient conditions
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ISSN0018-9286
1558-2523
DOI10.1109/TAC.2010.2041987

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Summary: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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2010.2041987