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Observer Design for One-Sided Lipschitz Nonlinear Systems Subject to Measurement Delays

Author

Listed:
  • Sohaira Ahmad
  • Raafia Majeed
  • Keum-Shik Hong
  • Muhammad Rehan

Abstract

This paper presents a novel nonlinear observer-design approach to one-sided Lipschitz nonlinear systems in the presence of output delays. The crux of the approach is to overcome the practical consequences of time delays, encountered due to distant sensor position and time lag in measurement, for estimation of physical and engineering nonlinear system states. A Lyapunov-Krasovskii functional is employed, the time derivative of which is solved using Jensen’s inequality, one-sided Lipschitz condition, and quadratic inner-boundedness, and, accordingly, design conditions for delay-range-dependent nonlinear observer for delayed one-sided Lipschitz systems are derived. Further, novel solutions to the problems of delay-dependent observer synthesis of one-sided Lipschitz models and delay-range-dependent state estimation of linear and Lipschitz nonlinear systems are deduced from the present delay-range-dependent technique. An observer formulation methodology for retrieval of one-sided Lipschitz nonlinear-system states, which is robust against norm-bounded perturbations, is devised. The resultant design conditions, in contrast to the conventional procedures, can be solved via less conservative linear matrix inequality- (LMI-) based routines that succeed by virtue of additional LMI variables, meaningful transformations, and cone complementary linearization algorithm. Numerical examples are worked out to illustrate the effectiveness of the proposed observer-synthesis approach for delayed one-sided Lipschitz systems.

Suggested Citation

  • Sohaira Ahmad & Raafia Majeed & Keum-Shik Hong & Muhammad Rehan, 2015. "Observer Design for One-Sided Lipschitz Nonlinear Systems Subject to Measurement Delays," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-13, March.
  • Handle: RePEc:hin:jnlmpe:879492
    DOI: 10.1155/2015/879492
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    Cited by:

    1. Rehan, Muhammad & Tufail, Muhammad & Hong, Keum-Shik, 2016. "Delay-range-dependent synchronization of drive and response systems under input delay and saturation," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 197-207.
    2. 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 1-30, April.

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