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Observer-based mixed \({{H}_{\infty }/{\text {passive}}}\) adaptive sliding mode control for Semi-Markovian jump system with time-varying delay

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Abstract

The work investigates the issue of mixed \({H_\infty }/{\text {passive}}\) adaptive sliding mode control (SMC) for continuous-time non-linear semi-Markovian jump systems (s-MJSs), which subject to mode-dependent time-varying delay, uncertainties, and external disturbance. An observer is developed first to reconstructed the state vector due to the states are always cannot be completely measured in the real system. Then on the probability space, an integral sliding surface function is raised. Furthermore, based on a new mode-dependent Lyapunov–Krasovskii function and the new sliding mode dynamic equation composed of error systems and observer systems, the required sufficient conditions are established to ensure the stochastic stability as well as the mixed \({H_\infty }\) and passive performance of the closed-loop system by using linear matrix inequality technique. Moreover, adaptive controllers are designed to guarantee the accessibility of the predefined sliding mode surface. Finally, the availability and less conservatism of the theoretical method we put forward can be testified by introducing the numerical examples.

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Acknowledgements

This work is partially supported by the National Natural Science Foundation of China no. 61273004, and the Natural Science Foundation of Hebei province no. F2018203099.

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Authors and Affiliations

  1. School of Science, Yanshan University, Qinhuangdao, 066004, Hebei, People’s Republic of China

    Zhiqi Wei, Huan Li & Yuechao Ma

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  1. Zhiqi Wei
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  2. Huan Li
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  3. Yuechao Ma
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Correspondence to Yuechao Ma.

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Communicated by Enrique Zuazua.

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This work is partially supported by the National Natural Science Foundation of China, under Grant number 61273004, and partially by the Natural Science Foundation of Hebei province no. F2018203099.

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Wei, Z., Li, H. & Ma, Y. Observer-based mixed \({{H}_{\infty }/{\text {passive}}}\) adaptive sliding mode control for Semi-Markovian jump system with time-varying delay. Comp. Appl. Math. 40, 287 (2021). https://doi.org/10.1007/s40314-021-01615-2

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