Robust Stochastic Stability and
Control for Uncertain Singular Markovian Jump Systems with Multiplicative Noise |
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| Authors: | Yong Zhao Weihai Zhang Jianwei Xia Tianliang Zhang |
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| Affiliation: | 1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, China;2. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, China;3. School of Mathematics Science, Liaocheng University, Liaocheng, China;4. College of Information and Control Engineering, China University of Petroleum (East China), Qingdao, China |
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| Abstract: | This paper focuses on the problems of robust stability and stabilization and robust  control for uncertain singular Markovian jump systems with (x,v)‐dependent noise. The parameter uncertainties appearing in state, input, disturbance as well as diffusion terms are assumed to be time‐varying but norm‐bounded. Based on the approach of generalized quadratic stability, the memoryless state feedback controller is designed for the robust stabilization problem, which ensures that the resulting closed‐loop system has an impulse‐free solution and is asymptotically stable in the mean square. Furthermore, the results of robust  control problem are derived. The desired state feedback  controller is presented, which not only meets the requirement of robust stabilization but also satisfies a prescribed  performance level. The obtained results are formulated in terms of strict LMIs. What we have obtained can be viewed as corresponding extensions of existing results on uncertain singular systems. A numerical example is finally given to demonstrate the application of the proposed method. |
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| Keywords: | singular Markovian jump systems robust stochastic stability and stabilization robust
control generalized quadratic stability linear matrix inequality |
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control for uncertain singular Markovian jump systems with (x,v)‐dependent noise. The parameter uncertainties appearing in state, input, disturbance as well as diffusion terms are assumed to be time‐varying but norm‐bounded. Based on the approach of generalized quadratic stability, the memoryless state feedback controller is designed for the robust stabilization problem, which ensures that the resulting closed‐loop system has an impulse‐free solution and is asymptotically stable in the mean square. Furthermore, the results of robust 
control problem are derived. The desired state feedback 
controller is presented, which not only meets the requirement of robust stabilization but also satisfies a prescribed 
performance level. The obtained results are formulated in terms of strict LMIs. What we have obtained can be viewed as corresponding extensions of existing results on uncertain singular systems. A numerical example is finally given to demonstrate the application of the proposed method.