H ∞ control for discrete-time nonlinear Markov jump systems with multiplicative noise and sector constraint
Corresponding Author
Hongji Ma
The Seventh Research Division, the Department of Systems and Control, LMIB, Beihang University (BUAA), Beijing, 100083, P.R. China
College of Science, Shandong University of Science and Technology, Qingdao, 266590, P.R. China
Correspondence to: Hongji Ma, The Seventh Research Division, the Department of Systems and Control, LMIB, Beihang University (BUAA), Beijing, 100083, P.R. China.
E-mail: [email protected]
Search for more papers by this authorYingmin Jia
The Seventh Research Division, the Department of Systems and Control, LMIB, Beihang University (BUAA), Beijing, 100083, P.R. China
Search for more papers by this authorCorresponding Author
Hongji Ma
The Seventh Research Division, the Department of Systems and Control, LMIB, Beihang University (BUAA), Beijing, 100083, P.R. China
College of Science, Shandong University of Science and Technology, Qingdao, 266590, P.R. China
Correspondence to: Hongji Ma, The Seventh Research Division, the Department of Systems and Control, LMIB, Beihang University (BUAA), Beijing, 100083, P.R. China.
E-mail: [email protected]
Search for more papers by this authorYingmin Jia
The Seventh Research Division, the Department of Systems and Control, LMIB, Beihang University (BUAA), Beijing, 100083, P.R. China
Search for more papers by this authorSUMMARY
This paper addresses the finite horizon H ∞ control problem for a class of discrete-time nonlinear Markov jump systems with multiplicative noise and nonlinear feedback device. The system nonlinearity occurs in a random way specified by a Bernoulli process, whereas the actuator and sensor nonlinearities are restricted to a sector region. Both the state and the dynamic output feedback H ∞ controllers are devised in terms of difference LMIs. The proposed approach not only allows the resulting system to achieve a prescribed disturbance attenuation level, but also enables the output of actuator/sensor to meet the designated sector condition. Moreover, it is also shown that our approach is well-adapted for dealing with the discrete-time Markov jump systems with saturated actuator and sensor. Finally, a backward iterative algorithm is provided to solve the obtained difference LMIs and a numerical example is presented to verify the efficiency of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.
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