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Non-fragile saturation control of nonlinear positive Markov jump systems with time-varying delays

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Abstract

This paper investigates non-fragile saturation control of nonlinear positive Markov jump systems, which contain sector nonlinear functions and time-varying delays. The saturation controller to be designed is supposed to have either multiplicative or additive gain uncertainty. First, a sufficient condition for the positivity of an auxiliary nonlinear system with sector restriction is established. By employing a nonlinear co-positive-type Lyapunov functional, a non-fragile control of the considered systems with multiplicative and additive perturbations is proposed in terms of linear programming, respectively. A set of non-fragile state feedback controllers associated with auxiliary feedback gains is designed using a matrix decomposition technique. Based on the designed controllers, the corresponding closed-loop systems are positive and stable with an \(L_{1}\)-gain performance and the system states converge to a cone set. Furthermore, an optimization method is developed to estimate the maximum invariant set. Compared with existing results, the proposed technique is not only less conservative but also reliable in practice. Finally, two simulation examples are provided to show the effectiveness of the obtained results.

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Acknowledgements

This work was supported in part by the National Nature Science Foundation of China (Nos. 61873314, 61503107, and 61673149), the Foundation of Key Laboratory of System Control and Information Processing, Ministry of Education China (No. Scip201803), and the Foundation of Zhejiang Provincial Education Department (No. Y201840738).

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Authors and Affiliations

  1. School of Automation, Hangzhou Dianzi University, Hangzhou, 310018, China

    Junfeng Zhang & Shicheng Li

  2. Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, 200240, China

    Junfeng Zhang

  3. Cedric-Lab, Conservatoire National des Arts et Métiers, 75141, Paris, France

    Tarek Raïssi

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  1. Junfeng Zhang
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Correspondence to Junfeng Zhang.

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Zhang, J., Raïssi, T. & Li, S. Non-fragile saturation control of nonlinear positive Markov jump systems with time-varying delays. Nonlinear Dyn 97, 1495–1513 (2019). https://doi.org/10.1007/s11071-019-05068-5

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