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$ \mathcal{H}_{\infty} $ control for fuzzy markovian jump systems based on sampled-data control method

  • * Corresponding author: Jianwei Xia

    * Corresponding author: Jianwei Xia 
The first author is supported by the National Natural Science Foundation of China under Grants 61573177, 61773191, 61973148
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  • This paper investigates the problems of $ \mathcal{H}_{\infty} $ performance analysis and sampled-data control about fuzzy Markovian jump systems. Firstly, in order to make full use of the information of both intervals $ x(t_{k}) $ to $ x(t) $ and $ x(t) $ to $ x(t_{k+1}) $, we construct the mode-dependent Lyapunov function, which consists of a two-sided closed-loop function. Built on the above Lyapunov function, the stochastically stable conditions with less conservative are given by using linear matrices inequalities (LMIs). Then, a state feedback controller is presented for the studied systems. At last, an example is offered to illustrate the efficiency of our main results.

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

    Citation:

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  • Table 1.  $ \gamma_{max} $ for $ h_{min} = 0 $ and different $ h_{max} $

    $ h_{max} $ 0.05 0.15 0.25 0.35
    $ \gamma $ $ 1.7320 $ 1.7678 1.8246 1.9285
     | Show Table
    DownLoad: CSV

    Table 2.  $ \gamma_{max} $ for $ h_{max} = h_{min} $

    $ h $ 0.05 0.15 0.25 0.35
    $ \gamma $ $ 1.7299 $ 1.7576 1.7982 1.8659
     | Show Table
    DownLoad: CSV
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