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Dissipative control for uncertain singular markovian jump systems via hybrid impulsive control

  • * Corresponding author: lh8481@tom.com; wangxingan@dlu.edu.cn

    * Corresponding author: lh8481@tom.com; wangxingan@dlu.edu.cn 
The first author is supported by National Natural Science Foundation of China (No.61802040), Natural Science Foundation of Liaoning Province (No.20180551241) and High-level Talent Innovation Support Program of Dalian City (No.2018RQ75). The second author is supported by National Key Laboratory for Precision Hot Processing of Metals(No.614290903061808) and Doctoral Starting Foundation of Dalian University (No.2017QL024)
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  • This paper investigates the problem of dissipative control for a class of uncertain singular Markovian jump systems. Different from the traditional control strategy, a derivative gain and impulsive control part are added in the proposed controller. A linearization approach via congruence transformations is proposed to solve the feedback design problem. In addition, the derived results contain $ H_{\infty} $ and passive control as special cases. Finally, examples are provided to illustrate the effectiveness and applicability of the proposed methods.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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  • Figure 1.  The Markov process

    Figure 2.  The state trajectories of the open-loop system (when $ \omega(t) = 0 $)

    Figure 3.  The state trajectories of the closed-loop system (when $ \omega(t) = 0 $)

    Table 1.  Minimum attenuation level calculated by different methods

    $ \gamma_{min} $ $ \rho=-0.5 $ $ \rho=0 $ $ \rho=0.5 $ $ \rho=1 $ $ \rho=1.5 $
    Theorem 10 ([28]) 1.2704 1.5821 2.2548 4.4628 ————
    Corollary 3.4 ($ K_{ei}=0 $) 1.1724 1.1738 1.1743 1.1749 1.1753
    Corollary 3.4 ($ K_{ei}\neq0 $) 1.1040 1.1050 1.1059 1.1067 1.1074
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