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<p>This paper addresses the exponential synchronization problem of nonlinear discrete-time complex dynamical networks subject to communication delays via an impulsive distributed control strategy. Unlike existing studies that neglect impulsive delays or rely on continuous-time formulations, we propose a new delayed impulsive control framework that explicitly incorporates reaction-time delay at impulsive instants. By employing Lyapunov stability theory and matrix inequality techniques, sufficient conditions are established to guarantee exponential synchronization under variable sampling periods, coupling strengths, and pinning gains. The derived results not only extend existing impulsive synchronization criteria to discrete-time delayed networks, but also provide flexible design guidelines for impulsive intervals and delay compensation. Moreover, several special cases-including fixed delays and undirected topologies are presented to illustrate the generality of the theoretical framework. Finally, a simulation example is presented to validate the effectiveness of the theoretical results.</p>

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Synchronization of discrete-time complex dynamical networks with delays via impulsive distributed control

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Zhihui Ma,
  • Kok Lay Teo,
  • Lei Wang,
  • Chen Wu,
  • Qian Li

摘要

This paper addresses the exponential synchronization problem of nonlinear discrete-time complex dynamical networks subject to communication delays via an impulsive distributed control strategy. Unlike existing studies that neglect impulsive delays or rely on continuous-time formulations, we propose a new delayed impulsive control framework that explicitly incorporates reaction-time delay at impulsive instants. By employing Lyapunov stability theory and matrix inequality techniques, sufficient conditions are established to guarantee exponential synchronization under variable sampling periods, coupling strengths, and pinning gains. The derived results not only extend existing impulsive synchronization criteria to discrete-time delayed networks, but also provide flexible design guidelines for impulsive intervals and delay compensation. Moreover, several special cases-including fixed delays and undirected topologies are presented to illustrate the generality of the theoretical framework. Finally, a simulation example is presented to validate the effectiveness of the theoretical results.