Synchronization Control of Networked Two-Timescale Dynamic Agents : A Singular Perturbation Approach

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Original languageEnglish
Pages (from-to)3-17
Number of pages15
Journal / PublicationIEEE Transactions on Control of Network Systems
Issue number1
Online published4 Jul 2023
Publication statusPublished - Mar 2024


This article is intended to solve the synchronization control problem for a group of agents with two-timescale characteristic, described by singularly perturbed systems (SPSs) with a small singular perturbation parameter ε. Three fundamental and yet challenging questions are addressed: 1) how to design a distributed controller to guarantee synchronization of coupled two-timescale agents for ε∈(0,ε∗) , where the stability bound ε∗ has to be determined?; 2) how to enlarge the stability bound ε∗ for a given feedback gain matrix?; and 3) how to cope with the situation when the singular perturbation parameter exceeds the prescribed stability bound ε∗? First, a decoupled method is applied to transfer the synchronization problem of networked two-timescale dynamic agents to the stability problem of SPSs associated with the eigenvalues of the network Laplacian matrix. Second, based on a specially constructed Lyapunov function, sufficient conditions are derived for simultaneously stabilizing the decoupled systems and computing ε∗ by utilizing a particle swarm optimization (PSO)-assisted method. Third, with the derived feedback gain matrix, some criteria are established to further enlarge the stability bound ε∗. Then, an integrated algorithm is developed to design a distributed controller with an even larger stability bound ε∗. Fourth, a novel network design method, incorporated with the concept of synchronization region, is proposed as a powerful solution to deal with the case when the feedback gain matrix is incapable of stabilizing the system. Finally, three examples are given to verify the theoretical results. © 2023 IEEE.

Research Area(s)

  • Circuit stability, Couplings, Eigenvalues and eigenfunctions, Networked two-timescale agents, Perturbation methods, singularly perturbed system, stability bound problem, Stability criteria, Symmetric matrices, Synchronization, synchronization control, singularly perturbed system (SPS)