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New Approach to \(H_{\infty }\) State Estimation for Continuous-Time Nonhomogeneous Markov Jump Systems with Time-Varying Delay

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Abstract

This paper investigates the \(H_{\infty }\) state estimation problem of continuous-time delayed nonhomogeneous Markov jump systems (NMJSs). To fully consider the nonhomogeneous transition rates (TRs) and state-related vectors, a parameter-dependent Lyapunov–Krasovskii functional (PDLKF) with triple integrals is constructed, in which the integrands in the PDLKF are all time-varying. In order to deal with the derivative of the time-varying integrands, a switched vertices approach is proposed to relax the bound assumptions in the existing works, which leads to more practical results. Based on these ingredients, a corresponding switched estimator approach is proposed to match an \(H_{\infty }\) estimator for NMJSs. The designed \(H_{\infty }\) estimator is related to the switched rule, which is more general than nonswitched estimators in the previous works. Some examples are illustrated to show the effectiveness of the obtained results.

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No data, models, or code were generated or used during the study.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 61973070, Liaoning Revitalization Talents Program under Grant XLYC1802010, in part by SAPI Fundamental Research Funds under Grant 2018ZCX22, and in part by the Fundamental Research Funds for the Central Universities under Grant N2104003.

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Authors and Affiliations

  1. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China

    Yufeng Tian, Zhanshan Wang & Changlai Wang

  2. Yangzhou Deyun Electrical Equipment Group Co., Ltd., Yangzhou, 225127, China

    Changlai Wang

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  1. Yufeng Tian
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Correspondence to Zhanshan Wang.

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Tian, Y., Wang, Z. & Wang, C. New Approach to \(H_{\infty }\) State Estimation for Continuous-Time Nonhomogeneous Markov Jump Systems with Time-Varying Delay. Circuits Syst Signal Process 41, 4390–4412 (2022). https://doi.org/10.1007/s00034-022-01995-8

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