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Stability and implementable ℋ∞ filters for singular systems with nonlinear perturbations

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Abstract

In this paper, we investigate the problem of designing ℋ∞ filter for a class of continuous-time uncertain singular systems with nonlinear perturbations, which can be realized in practice. The perturbation is a time-varying function of the system state and satisfies a Lipschitz constraint. The design objective is to guarantee that a prescribed upper bound on an ℋ∞ performance of the robust filter is attained for all possible energy-bounded input disturbances and all admissible uncertainties and which can be implemented on-line to get a good replica of the state. We first establish sufficient condition for the existence and uniqueness of solution to the singular system connected with the normal filter. Using a linear matrix inequality (LMI) format, we then provide a sufficient condition for the asymptotic stability of the realizable ℋ∞ filter. Then by means of a convex analysis procedure the filter gain matrices are derived and an important special case is readily deduced. Finally, a numerical example is presented to illustrate the theoretical developments.

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Authors and Affiliations

  1. Systems Engineering Department, King Fahd University of Petroleum and Minerals, P.O. Box 985, Dhahran, 31261, Saudi Arabia

    Magdi S. Mahmoud

  2. Electrical Engineering Department, Kuwait University, P.O. Box 5969, Safat, 13060, Kuwait

    Naif B. Almutairi

Authors
  1. Magdi S. Mahmoud
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  2. Naif B. Almutairi
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Correspondence to Magdi S. Mahmoud.

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Mahmoud, M.S., Almutairi, N.B. Stability and implementable ℋ∞ filters for singular systems with nonlinear perturbations. Nonlinear Dyn 57, 401–410 (2009). https://doi.org/10.1007/s11071-008-9450-3

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  • DOI: https://doi.org/10.1007/s11071-008-9450-3

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