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Decentralized Observer-Based Reliable Control for a Class of Interconnected Markov Jumped Time-Delay System Subject to Actuator Saturation and Failure

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Abstract

A decentralized stabilization method is investigated for a class of interconnected Markov jumping systems subject to time-varying delays, actuator saturation and jumped failure. The mean-square exponential stability condition is established by constructing multiple Lyapunov–Krasovskii functionals, which are delay-dependent, mode-dependent and decay rate-dependent. Taking into account the influence of actuator saturation and jumped actuator failure, decentralized observer-based \( H_{\infty } \) state feedback stabilization schemes are designed. The decentralized observer gains and controller gains are determined by solving a convex optimization problem with \( H_{\infty } \) performance \( \gamma^{2} \) as objective and LMIs as constraints. Simulation results are also presented to illustrate the effectiveness and applicability of the obtained results.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant No. 51277022, Chongqing Education Council Foundation under Grant Nos. KJ1501312 and KJ1601310, Chongqing University of Science and Technology doctoral Foundation under Grant No. CK2016B17, and China Scholarship Council under Grant No. 201608505169.

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Authors and Affiliations

  1. Department of Mathematics and Physics, Chongqing University of Science and Technology, Chongqing, 401331, China

    Zhaohui Chen

  2. School of Physics and Electronic Engineering, Guangzhou University, Guangzhou, 510006, China

    Zhong Cao

  3. Sichuan Provincial Key Lab of Power System Wide-Area Measurement and Control, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Qi Huang

  4. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695-8205, USA

    Stephen L. Campbell

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  1. Zhaohui Chen
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  2. Zhong Cao
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  4. Stephen L. Campbell
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Correspondence to Stephen L. Campbell.

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Chen, Z., Cao, Z., Huang, Q. et al. Decentralized Observer-Based Reliable Control for a Class of Interconnected Markov Jumped Time-Delay System Subject to Actuator Saturation and Failure. Circuits Syst Signal Process 37, 4728–4752 (2018). https://doi.org/10.1007/s00034-018-0795-7

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