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Volume 7 Issue 3
Apr.  2020

IEEE/CAA Journal of Automatica Sinica

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Younes Solgi, Alireza Fatehi and Ala Shariati, "Non-Monotonic Lyapunov-Krasovskii Functional Approach to Stability Analysis and Stabilization of Discrete Time-Delay Systems," IEEE/CAA J. Autom. Sinica, vol. 7, no. 3, pp. 752-763, May 2020. doi: 10.1109/JAS.2020.1003102
Citation: Younes Solgi, Alireza Fatehi and Ala Shariati, "Non-Monotonic Lyapunov-Krasovskii Functional Approach to Stability Analysis and Stabilization of Discrete Time-Delay Systems," IEEE/CAA J. Autom. Sinica, vol. 7, no. 3, pp. 752-763, May 2020. doi: 10.1109/JAS.2020.1003102

Non-Monotonic Lyapunov-Krasovskii Functional Approach to Stability Analysis and Stabilization of Discrete Time-Delay Systems

doi: 10.1109/JAS.2020.1003102
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  • In this paper, a novel non-monotonic Lyapunov-Krasovskii functional approach is proposed to deal with the stability analysis and stabilization problem of linear discrete time-delay systems. This technique is utilized to relax the monotonic requirement of the Lyapunov-Krasovskii theorem. In this regard, the Lyapunov-Krasovskii functional is allowed to increase in a few steps, while being forced to be overall decreasing. As a result, it relays on a larger class of Lyapunov-Krasovskii functionals to provide stability of a state-delay system. To this end, using the non-monotonic Lyapunov-Krasovskii theorem, new sufficient conditions are derived regarding linear matrix inequalities (LMIs) to study the global asymptotic stability of state-delay systems. Moreover, new stabilization conditions are also proposed for time-delay systems in this article. Both simulation and experimental results on a pH neutralizing process are provided to demonstrate the efficacy of the proposed method.

     

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    Highlights

    • A novel less conservative non-monotonic Lyapunov-Krasovskii stability approach is proposed for stability analysis of discrete time-delay systems.
    • A novel stabilization algorithm is derived based on the introduced non-monotonic stability condition.
    • Linear Matrix Inequalities (LMI) and Iterative LMI based nonlinear minimization are used to obtain the Lyapunov-Krasovskii functional and the controller respectively.
    • The proposed method is experimentally evaluated on a pH neutralization process.

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