High-order moment stabilization for Markov jump systems with attenuation rate |
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| Institution: | 1. School of Aeronautics and Astronautics, Shanghai Jiaotong University, Dongchuan Rd. No. 800, Shanghai 200240, China;2. Chengdu Aircraft Design and research Institute (CADI), Riyue Avenue No.1610, Chengdu 610091, China;1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China;2. Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China;1. Department of Electrical and Computer Engineering, COMSATS University Islamabad (Lahore Campus), Lahore 54000, Pakistan;2. College of Energy and Electrical Engineering, Hohai University, Nanjing 210098, People’s Republic of China |
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| Abstract: | This paper studies the high-order moment control problem for discrete-time Markov jump linear systems (MJLSs) with certain dynamic response performance and disturbance rejection specifications. An appropriate cumulant generating function is employed to express the original stochastic system in high-order component form. This facilities the high-order moment stabilization of MJLSs. Moreover, a pole region assignment approach is utilized to ensure desired dynamic response specifications with a certain attenuation rate. An arithmetic and geometric inequality approach is utilized to extract sufficient conditions ensuring the designed controller existence. These conditions ensure the high-order moment steady-state property and certain dynamic specifications for the MJLSs. The effectiveness of the proposed method is demonstrated through numerical and practical examples. |
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