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Observer Design for One-sided Lipschitz Uncertain Descriptor Systems with Time-varying Delay and Nonlinear Uncertainties

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Abstract

This paper investigates observer design for a class of one-sided Lipschitz descriptor systems with time-varying delay and uncertain parameters. In order to provide a general framework for large-scale systems, the paper considers uncertainties, nonlinearities, disturbance and time-varying delay at both output and state. By constructing Lyapunov–Krasovskii functional, and using the one-sided Lipschitz condition and the quadratic inner-boundedness inequality, we establish the sufficient condition which guarantees that the observer error dynamics is asymptotically stable, and the proposed observer ensures the \(L_2\) gain bounded by a scalar \(\gamma .\) Then, we change the condition into a strict matrix inequality condition. Furthermore, based on the obtained results, we establish the linear matrix inequality-based condition to ensure the asymptotically convergence of state estimation error and to accomplish robustness against \(L_2\) norm bounded disturbances by utilizing change of variables. We propose the computing method of observer gain. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method.

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Acknowledgements

This work was supported by the Natural Science Foundation of Tianjin under Grant no. 18JCYBJC88000 and the Qinghai Science and Technology Department, Grant/Award Number: 2017-ZJ-Y27.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tiangong University, Tianjin, 300387, China

    Yali Dong, Jing Hao & Mengxiao Deng

  2. New Energy Photovoltaic Industry Research Center, Qinghai University, Xining, 810016, China

    Shengwei Mei

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  1. Yali Dong
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  2. Jing Hao
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Correspondence to Yali Dong.

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Dong, Y., Hao, J., Mei, S. et al. Observer Design for One-sided Lipschitz Uncertain Descriptor Systems with Time-varying Delay and Nonlinear Uncertainties. Circuits Syst Signal Process 40, 4779–4798 (2021). https://doi.org/10.1007/s00034-021-01703-y

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