This paper is concerned with the observer-based prescribed-time synchronization and topology identification issue for complex networks of nonlinear impulsive piecewise-smooth systems (IPWSs), where the stabilizing and destabilizing impulses are considered simultaneously. A prescribed-time convergence principle is developed for nonlinear IPWSs on the basis of a power exponent function. A controller with time-varying feedback gains and a topology observer are designed to realize the prescribed-time synchronization and identification objective. By applying the Lyapunov stability theory and non-smooth analysis approach, the prescribed-time synchronization conditions are addressed, and the unknown topology is identified successfully through the topology observer. Finally, a simulation example is presented to show the effectiveness of the proposed strategy and the validity of the theoretical results.

本文关注非线性脉冲分段平滑系统（IPWS）复杂网络的基于观测器的规定时间同步和拓扑识别问题，其中同时考虑稳定和不稳定脉冲。基于幂指数函数，为非线性 IPWS 开发了规定时间收敛原理。设计了具有时变反馈增益的控制器和拓扑观测器，以实现规定时间的同步和识别目标。应用Lyapunov稳定性理论和非光滑分析方法，解决了规定时间同步条件，并通过拓扑观测器成功识别了未知拓扑。最后通过仿真算例验证了所提策略的有效性和理论结果的有效性。