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Disturbance Rejection for Markov Jump Systems with Partly Unknown Transition Probabilities and Saturation

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Abstract

This paper mainly investigates the disturbance rejection problem of Markov jump systems with bounded disturbance and saturation, in the case that only part of the transition probabilities are known in the discrete-time domain. The mode-dependent state feedback controller is designed to ensure that the resulting closed-loop system is stochastically stable and satisfies the optimal disturbance rejective index, meanwhile, the state of the system is to remain in an expected small region including origin in terms of disturbances. Specifically, the stochastically stable conditions are formulated by parameter-dependent Lyaponuv methodology and further established as linear matrix inequalities (LMIs). Sweeping the auxiliary parameters in the domain of definition, the global optimal disturbance rejective index is obtained. Finally, tolerance capability is further analyzed to evaluate the disturbance rejection level. Two numerical examples, a common linear system and a Markov jump system with completely known and partly unknown transition probabilities, are presented to illustrate the potential of the results, respectively.

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Acknowledgements

This work was partially supported by National Natural Science Foundation of China (61273087, 61134007), Program for Excellent Innovative Team of Jiangsu Higher Education Institutions, Jiangsu Higher Education Institutions Innovation Funds (CXZZ12−0743), the Fundamental Research Funds for the Central Universities (JUDCF12029).

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  1. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Institute of Automation, Jiangnan University, Wuxi, 214122, PR China

    Yanqing Liu & Fei Liu

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  1. Yanqing Liu
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  2. Fei Liu
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Correspondence to Fei Liu.

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Liu, Y., Liu, F. Disturbance Rejection for Markov Jump Systems with Partly Unknown Transition Probabilities and Saturation. Circuits Syst Signal Process 32, 2783–2797 (2013). https://doi.org/10.1007/s00034-013-9593-4

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