Novel Non-monotonic Lyapunov-Krasovskii Based Stability Analysis and Stabilization of Discrete State-delay System
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Non-monotonic Lyapunov-Krasovskii Based Stability Analysis and Stabilization of Discrete State-delay System Younes Solgi Alireza Fatehi Ala Shariati APAC Research Group, Industrial Control Center of Excellence, Faculty of Electrical Engineering, K.N. Toosi University of Technology, Tehran, 1631714191 Iran
Abstract: This paper proposes a novel less-conservative non-monotonic Lyapunov-Krasovskii stability approach for stability analysis of discrete time-delay systems. In this method, monotonically decreasing requirements of the Lyapunov-Krasovskii method are replaced with non-monotonic ones. The Lyapunov-Krasovskii functional is allowed to increase in some steps, but the overall trend should be decreasing. The model of practical systems used for stability analysis usually contain uncertainty. Therefore, firstly a non-monotonic stability condition is derived for certain discrete time-delay systems, then robust non-monotonic stability conditions are proposed for uncertain systems. Finally, a novel stabilization algorithm is derived based on the introduced non-monotonic stability condition. The Lyapunov-Krasovskii functional and the controller are obtained by solving a set of linear matrix inequalities (LMI) or iterative LMI based nonlinear minimization. The proposed theorems are first evaluated by some numerical examples, and then by simulation and implementation on the pH neutralizing process plant. Keywords: Lyapunov-Krasovskii functional, discrete state-delay systems, non-monotonic Lyapunov function, robust stability, stabilization.
1 Introduction One of the most important methods for stability analysis of time-delay systems is the Lyapunov based approach[1, 2], which has been very successful and applicable in control engineering. Nevertheless, the determination of a proper and less conservative Lyapunov functional (LF) for different types of systems is still a serious challenge. This will be more challenging in time-delay systems. Time-delay systems depend not only on the present states but also on the past d steps of the states. Therefore, stability analysis of time-delay systems requires LyapunovKrasovskii functional (LKF) rather than Lyapunov function. Many studies have focused on Lyapunov-Krasovskii stability methods to reduce conservatism by some modifications[2]. These modifications are usually completed by adding new summation terms to the equations that arise in the stability analysis procedure. Therefore, a popular conservatism reduction method is estimating a smaller upper bound for common summation terms appearing in the forward difference of a Lyapunov–Krasovskii functional[3]. Considerable progress has been made in finding an LKF for stability analysis and controller design for Research Article Manuscript received September 16, 2019; accepted January 7, 2020 Recommended by Associate Editor Jie zhang © Institute of Automation, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2020
discrete-time
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