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Unknown input observer design for one-sided Lipschitz discrete-time systems subject to time-delay

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  • Nguyen, Minh Cuong
  • Trinh, Hieu

Abstract

In this paper, we address the problem of unknown input observer design, which simultaneously estimates state and unknown input, of a class of nonlinear discrete-time systems with time-delay. A novel approach to the state estimation problem of nonlinear systems where the nonlinearities satisfy the one-sided Lipschitz and quadratically inner-bounded conditions is proposed. This approach also allows us to reconstruct the unknown inputs of the systems. The nonlinear system is first transformed to a new system which can be decomposed into unknown-input-free and unknown-input-dependent subsystems. The estimation problem is then reduced to designing observer for the unknown-input-free subsystem. Rather than full-order observer design, in this paper, we propose observer design of reduced-order which is more practical and cost effective. By utilizing several mathematical techniques, the time-delay issue as well as the bilinear terms, which often emerge when designing observers for nonlinear discrete-time systems, are handled and less conservative observer synthesis conditions are derived in the linear matrix inequalities form. Two numerical examples are given to show the efficiency and high performance of our results.

Suggested Citation

  • Nguyen, Minh Cuong & Trinh, Hieu, 2016. "Unknown input observer design for one-sided Lipschitz discrete-time systems subject to time-delay," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 57-71.
    • Handle: RePEc:eee:apmaco:v:286:y:2016:i:c:p:57-71
    DOI: 10.1016/j.amc.2016.04.003
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    Cited by:

    1. Nguyen, Cuong M. & Pathirana, Pubudu N. & Trinh, Hieu, 2019. "Robust observer and observer-based control designs for discrete one-sided Lipschitz systems subject to uncertainties and disturbances," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 42-53.
    2. Ning, Jinghua & Hua, Changchun, 2022. "H∞ output feedback control for fractional-order T-S fuzzy model with time-delay," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    3. Nguyen, Cuong M. & Tan, Chee Pin & Trinh, Hieu, 2021. "State and delay reconstruction for nonlinear systems with input delays," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    4. Yanbin Zhao & Wenqiang Dong, 2024. "Feedback Stabilization of Quasi-One-Sided Lipschitz Nonlinear Discrete-Time Systems with Reduced-Order Observer," Mathematics, MDPI, vol. 12(10), pages 1-16, May.
    5. Yang, Yuxia & Lin, Chong & Chen, Bing & Wang, Qing-Guo, 2018. "Reduced-order observer design for a class of generalized Lipschitz nonlinear systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 267-280.

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