Robust impulse nonlinear delayed multi-agent systems: an exponential synchronization

Volume 34, Issue 2, pp 162--175 https://dx.doi.org/10.22436/jmcs.034.02.06

Publication Date: March 06, 2024 Submission Date: October 31, 2023 Revision Date: November 06, 2023 Accteptance Date: February 02, 2024

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Authors

N. Kaewbanjak - Faculty of Science at Sriracha, Kasetsart University, Sriracha Campus, Chon Buri, 20230, Thailand. A. Stephen - Center for Computational Modeling, Chennai Institute of Technology, Chennai-600 069, Tamil Nadu, India. A. Srinidhi - Department of Mathematics , Alagappa University, Karaikudi-630 004, India. R. Raja - Ramanujan Centre for Higher Mathematics , Alagappa University, Karaikudi-630 004, India. - Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon. K. Mukdasai - Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand. J. Thipcha - Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand. P. Singkibud - Department of Applied Mathematics and Statistics, Faculty of Science and Liberal Arts, Rajamangala University of Technology Isan, Nakhon Ratchasima 30000, Thailand.

Abstract

This work explores the use of state-feedback pinning control in the presence of time-varying delay to solve the synchronization problem of uncertain nonlinear multi-agent systems (MASs). To begin, it is assumed that the agent's communication topology is a directed, static network. Second, the synchronization issue is transformed into the typical closed-loop system stability issue by employing Laplacian matrix inequality (LMI). The primary goal of this study is to construct a state-feedback pinning controller that yields a closed-loop system that is stable under all permissible uncertainty and impulsive cases. To achieve this goal, we develop a new set of delay-dependent synchronization criteria for the closed-loop system by constructing an appropriate Lyapunov functional and making use of Kronecker product features in conjunction with matrix inequality approaches. All that's needed to construct the optimal state-feedback controller is a set of constraints in the form of linear matrix inequalities, which can be solved with any number of powerful optimization methods. To further illustrate the practicality and efficiency of the suggested control design system, a numerical example and associated simulations are provided.

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Keywords

• Multi-agent systems
• time delay
• parameter uncertainty
• linear matrix inequality
• exponential synchronization

MSC

•  34A34
•  26D10
•  34D20
•  92B20

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