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Non-fragile Observer-Based \({\mathcal {H}}_{\infty }\) Control for Discrete-Time Systems Using Passivity Theory

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Abstract

In this paper, non-fragile observer-based \({\mathcal {H}}_{\infty }\) controller design is investigated for a class of discrete-time systems. The system under consideration is assumed to have random fluctuations in both the state feedback controller gain and observer gain matrices. The random fluctuations are defined using Bernoulli-distributed white sequences with time-varying probability measures. The probability-dependent controller gains are designed to guarantee the stochastic stability of the system with a prescribed mixed \({\mathcal {H}}_{\infty }\) and passivity performance. Lyapunov stability theory, passivity theory and a linear matrix inequality (LMI) approach are used to derive sufficient conditions for the existence of the state feedback controller and observer gains. The probability-dependent gain-scheduled controllers are designed based on a convex optimization problem using a set of LMIs, which can be easily solved with standard numerical packages. Finally, a practical application is presented as an example to illustrate the effectiveness and potential of the method.

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Acknowledgments

We would like to thank the Editor-In-Chief, Prof. M. N. S. Swamy, the Associate Editor, and the Reviewers for the comments that helped to improve the quality of the paper. The work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2013R1A1A2A10005201).

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Authors and Affiliations

  1. Department of Electrical Engineering/Information and Communication Engineering, Yeungnam University, 280 Daehak-Ro, Kyongsan, 712-749, Republic of Korea

    K. Mathiyalagan, Ju H. Park & H. Y. Jung

  2. Department of Mathematics, Sungkyunkwan University, Suwon, 440 746, Republic of Korea

    R. Sakthivel

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  1. K. Mathiyalagan
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  2. Ju H. Park
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  3. H. Y. Jung
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  4. R. Sakthivel
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Correspondence to Ju H. Park.

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Mathiyalagan, K., Park, J.H., Jung, H.Y. et al. Non-fragile Observer-Based \({\mathcal {H}}_{\infty }\) Control for Discrete-Time Systems Using Passivity Theory. Circuits Syst Signal Process 34, 2499–2516 (2015). https://doi.org/10.1007/s00034-015-9984-9

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  • DOI: https://doi.org/10.1007/s00034-015-9984-9

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