H∞ Control for Nonlinear Stochastic Markov Systems with Time-Delay and Multiplicative Noise

This paper is concerned with the H∞ control problem for a class of nonlinear stochastic Markov jump systems with time-delay and system state-, control input-and external disturbancedependent noise. Firstly, by solving a set of Hamilton-Jacobi inequalities（HJIs）, the exponential mean square H∞ contro...

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Bibliographic Details
Published in:Journal of systems science and complexity 2017-12, Vol.30 (6), p.1293-1315
Main Authors: Wang, Yuhong, Pan, Zhiteng, Li, Yan, Zhang, Weihai
Format: Article
Language:English
Subjects:
Complex Systems
Control
Control systems design
Delay
Fuzzy systems
H-infinity control
Linear matrix inequalities
Markov chains
Mathematical analysis
Mathematics
Mathematics and Statistics
Mathematics of Computing
Matrix methods
Nonlinear control
Nonlinear systems
Operations Research/Decision Theory
Production planning
Statistics
Systems Theory
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Summary:This paper is concerned with the H∞ control problem for a class of nonlinear stochastic Markov jump systems with time-delay and system state-, control input-and external disturbancedependent noise. Firstly, by solving a set of Hamilton-Jacobi inequalities（HJIs）, the exponential mean square H∞ controller design of delayed nonlinear stochastic Markov systems is presented. Secondly,by using fuzzy T-S model approach, the H∞ controller can be designed via solving a set of linear matrix inequalities（LMIs） instead of HJIs. Finally, two numerical examples are provided to show the effectiveness of the proposed design methods.
ISSN:1009-6124
1559-7067
DOI:10.1007/s11424-017-6003-1