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Delay-range-dependent observer-based control of nonlinear systems under input and output time-delays

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  • Majeed, Raafia
  • Ahmad, Sohaira
  • Rehan, Muhammad

Abstract

The problem of designing observer-based controller for a class of nonlinear time-delay systems subjected to input and output time-varying delays is addressed in this paper. More incisively, a delay-range-dependent criterion, incorporating variation of delays between known lower and upper bounds, is established for control of nonlinear time-delay systems. The proposed methodology ensures asymptotic stability of the closed-loop system's state and the estimation error between states of the system and observer. By application of a Lyapunov–Krasovskii functional, Jensen's inequality, standard matrix inequality procedures, Luenberger-type observer, delay-interval bounds and delay-derivative limits, observer-based controller synthesis approach using nonlinear matrix inequalities for the nonlinear time-delay systems is provided. Further, a decoupling approach is employed to render a simpler condition for the observer and the controller synthesis. A novel observer-based control scheme for the linear time-delay systems with interval time-varying input as well as output lags is derived from the proposed control strategy. The traditional delay-dependent controller design, incorporating zero lower bound of the delay, for the time-delay systems is a particular scenario of the projected delay-range-dependent approach. The proposed decoupled observer-based controller synthesis condition is cast into linear matrix inequalities by means of the cone complementary linearization approach. Finally, a numerical simulation example of control of one-link flexible joint robotic arm is provided to verify the proposed design methodology.

Suggested Citation

  • Majeed, Raafia & Ahmad, Sohaira & Rehan, Muhammad, 2015. "Delay-range-dependent observer-based control of nonlinear systems under input and output time-delays," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 145-159.
  • Handle: RePEc:eee:apmaco:v:262:y:2015:i:c:p:145-159
    DOI: 10.1016/j.amc.2015.04.052
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    References listed on IDEAS

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    1. O. M. Kwon & J. H. Park & S. M. Lee & S. C. Won, 2006. "LMI Optimization Approach to Observer-Based Controller Design of Uncertain Time-Delay Systems via Delayed Feedback," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 103-117, January.
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    Cited by:

    1. Wang, Qingzhi & He, Yong & Tan, Guanzheng & Wu, Min, 2017. "Observer-based periodically intermittent control for linear systems via piecewise Lyapunov function method," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 438-447.
    2. Zhang, Juan & Zhang, Huaguang & Cai, Yuliang & Wang, Wei, 2021. "Consensus control for nonlinear multi-agent systems with event-triggered communications," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    3. Sohaira Ahmad & Muhammad Rehan & Anas Ibrar & Muhammad Umair Ali & Amad Zafar & Seong Han Kim, 2024. "Novel Robust Estimation-Based Control of One-Sided Lipschitz Nonlinear Systems Subject to Output and Input Delays," Mathematics, MDPI, vol. 12(9), pages 1-35, April.

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