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Robust generalized filtering of uncertain Lipschitz nonlinear systems under measurement delays

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Abstract

In the present study, a generalized structure for the robust filtering, which adequately addresses both the dynamic and the static-gain filter structures, is accounted for the uncertain Lipschitz nonlinear systems with the measurement delays, parametric uncertainties, and disturbances. The proposed robust filtering approach uses a Lyapunov–Krasovskii functional with a specialized stipulation for dealing with the measurement lags, employs a delay-range-dependent stability method for tackling the delayed dynamics, applies the upper bounds on norms of the uncertainties to deal with parametric variations, and explores the \(L_2 \) stability condition to handle the exogenous perturbations. The nonlinear dynamics is tempered by the direct infusion of the Lipschitz continuity, and uncertainties are modeled using bounds on the uncertain matrices norms to render a linear matrix inequality (LMI)-based design. The proposed filtering approaches establish the \(L_2 \) stability for the filtering error and efficaciously reckon the solution of unknown filter matrices using the LMI-oriented computational algorithms. Numerical simulation example is appended to manifest the effectuality of the proposed results.

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Acknowledgements

This work was supported by Higher Education Commission (HEC) of Pakistan by supporting Ph.D. studies of the first author through indigenous Ph.D. scholarship program (phase II, batch II, 2013).

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Authors and Affiliations

  1. Department of Electrical Engineering, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Islamabad, Pakistan

    Sohaira Ahmad & Muhammad Rehan

  2. Department of Computer and Information Sciences, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Islamabad, Pakistan

    Muhammad Iqbal

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  1. Sohaira Ahmad
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  2. Muhammad Rehan
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  3. Muhammad Iqbal
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Correspondence to Muhammad Rehan.

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Ahmad, S., Rehan, M. & Iqbal, M. Robust generalized filtering of uncertain Lipschitz nonlinear systems under measurement delays. Nonlinear Dyn 92, 1567–1582 (2018). https://doi.org/10.1007/s11071-018-4147-8

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