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Novel Non-monotonic Lyapunov-Krasovskii Based Stability Analysis and Stabilization of Discrete State-delay System

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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.

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Authors and Affiliations

  1. APAC Research Group, Industrial Control Center of Excellence, Faculty of Electrical Engineering, K.N. Toosi University of Technology, Tehran, 1631714191, Iran

    Younes Solgi, Alireza Fatehi & Ala Shariati

Authors
  1. Younes Solgi
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  2. Alireza Fatehi
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  3. Ala Shariati
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Corresponding author

Correspondence to Alireza Fatehi.

Additional information

Recommended by Associate Editor Jie zhang

Younes Solgi received the B. Sc. and M. Sc. degrees in electrical engineering from the Bu Ali Sina University, Hamedan, Iran in 2012 and 2014 recpectively. He is curently a Ph. D. degree candidate at K.N. Toosi University of Technology (KNTU), Tehran, Iran.

His research interests include stability analysis, process control systems, robust control, and intelligent systems.

Alireza Fatehi received the B. Sc. degree from the Isfahan University of Technology, Isfahan, Iran in 1990, the M. Sc. degree from Tehran University, Iran in 1995, and the Ph. D. degree from Tohoku University, Japan in 2001, all in electrical engineering. He is an associate professor of electrical engineering with the K.N. Toosi University of Technology (KNTU), Iran. He is the Director of Advanced Process Automation and Control Research Group and a member of the Industrial Control Center of Excellence, KNTU. From 2013 to 2015, he was a visiting profess- or with the Department of Chemical and Materials Engineering, University of Alberta, Canada.

His research interests include industrial control systems, process control systems, intelligent systems, multiple model controller, nonlinear predictive controller, nonlinear identification, fault detection, and soft sensor.

Ala Shariati received the B. Sc. degree in control engineering from Tehran University, Iran in 1998, and the M. Sc. and Ph. D. degrees in control engineering from K.N. Toosi University of Technology, Iran in 2003 and 2012, respectively. She was a Postdoctoral Fellow at University of Alberta from March to August 2014. She is currently a research assistant in APAC research group of K.N. Toosi University of Technology, Iran.

Her research interests include time-delay systems, robust control, multi-agent systems and teleoperation systems.

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Solgi, Y., Fatehi, A. & Shariati, A. Novel Non-monotonic Lyapunov-Krasovskii Based Stability Analysis and Stabilization of Discrete State-delay System. Int. J. Autom. Comput. 17, 713–732 (2020). https://doi.org/10.1007/s11633-020-1222-7

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