This article is concerned with quasi-synchronization of grid-connected systems in electrical networks, where heterogeneous Inductance-Capacitance (LC) oscillators are coupled via electrical inductance subject to time-varying delays. Note that complete synchronization fails to be accomplished due to the existence of nonidentical parameters and quasi-synchronization cannot be achieved via non-delayed inductive coupling. A configuration of multiple heterogeneous LC oscillators with inductive coupling subject to time-varying lumped delay is first constructed by introducing an active delay intentionally. Then the complete-type Lyapunov-Krasovskii functionals (LKF) are constructed to investigate the exponential convergence of quasi-synchronization of LC oscillators in the presence of parameter mismatches utilizing the positive effects of interval time-varying delays. Some feasible synchronization criteria are derived. The gain matrix can be designed by solving a set of linear matrix inequalities combining an optimization algorithm. Finally, a numerical example of five LC oscillators in photovoltaic grid-connected system is given to demonstrate the effectiveness of the proposed method.

中文翻译：

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故意改变时滞的并网系统中异构LC电路的准同步

本文涉及电网中的并网系统的准同步，在该系统中，异质电感电容（LC）振荡器通过电感耦合，但会受到时变延迟的影响。请注意，由于存在不相同的参数，因此无法完成完全同步，并且无法通过非延迟电感耦合来实现准同步。首先通过有意引入有源延迟来构造具有时变集总延迟的电感耦合的多个异构LC振荡器的配置。然后构造完整类型的Lyapunov-Krasovskii泛函（LKF），以利用间隔时变延迟的积极影响，研究在参数不匹配的情况下LC振荡器的准同步的指数收敛性。得出一些可行的同步标准。可以通过结合优化算法求解一组线性矩阵不等式来设计增益矩阵。最后，给出了光伏并网系统中五个LC振荡器的数值实例，以证明所提方法的有效性。