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\(H_\infty \) dynamic observer design for discrete-time linear systems with time varying delays based on generalized reciprocally convex matrix inequality

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Abstract

In this work, we have studied the problem of designing \(H_\infty \) dynamic observers (HDO) for discrete-time linear systems (DTLS) with time-varying delay (TVD) and disturbance. By designing an augmented Lyapunov-Krasovskii functional (LKF) with double summation terms using the Generalized reciprocally convex matrix inequality (GRCMI), as well as the Jensen-based inequality (JBI) and the Wirtinger-based inequality (WBI) that derive new less conservative time-dependent conditions. The resulting algebraic conditions form a set of linear matrix inequalities (LMIs) which can be solved by the LMI or YALMIP toolboxes. Furthermore, the observer under consideration has more degrees of freedom to be estimated, and is known as a generalized observer, where the proportional and proportional-integral observers are particular cases. Finally, two examples are given to demonstrate the validity and effectiveness of the findings.

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The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Authors and Affiliations

  1. National School of Applied Sciences, Sidi Mohamed Ben Abdellah University, BP 72, My Abdallah Avenue Km. 5 Imouzzer Road, Fez, 30000, Morocco

    Ghali Naami & Mohamed Ouahi

  2. Modeling Information, and Systems Laboratory, University of Picardie Jules Verne, 33 Rue St Leu, Amiens, 80000, France

    Abdelhamid Rabhi

  3. Higher School of Technology, University Med First Oujda, BP 473, Cité Al Qods, Oujda, 60000, Morocco

    Mohamed Larbi Elhafyani

Authors
  1. Ghali Naami
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  2. Mohamed Ouahi
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  3. Abdelhamid Rabhi
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  4. Mohamed Larbi Elhafyani
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Contributions

GN contributed to the methodology, formal analysis and writing of the original version; MO, AR and MLE review and editing.

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Correspondence to Ghali Naami.

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Naami, G., Ouahi, M., Rabhi, A. et al. \(H_\infty \) dynamic observer design for discrete-time linear systems with time varying delays based on generalized reciprocally convex matrix inequality. Int. J. Dynam. Control (2023). https://doi.org/10.1007/s40435-023-01305-3

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  • DOI: https://doi.org/10.1007/s40435-023-01305-3

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