This study examines the problem of impulsive and pinning control synchronization of Markovian jumping master-slave complex dynamical networks with hybrid coupling and additive interval time-varying delays. The linear couplings include both the discrete time-varying delay and the distributed time-varying delays. Two kinds of control schemes are utilized to synchronize the considered dynamical network system. Impulsive and pinning control strategies are designed to synchronize the master-slave complex networks. By applying Lyapunov stability theory, Jensen’s inequality, Schur complement and linear matrix inequality technique, some new delay-dependent conditions are derived to guarantee the asymptotic stability of this system. We provided numerical examples to illustrate the feasibility and effectiveness of the results obtained.

本研究探讨了具有混合耦合和加性区间时变时滞的马尔可夫跳跃主从复杂动力网络的脉冲和固定控制同步问题。线性耦合包括离散时变延迟和分布式时变延迟。利用两种控制方案来同步所考虑的动态网络系统。脉冲和固定控制策略旨在同步主从复杂网络。运用李雅普诺夫稳定性理论，詹森不等式，舒尔补码和线性矩阵不等式技术，推导了一些新的时滞相关条件，以保证系统的渐近稳定性。我们提供了数值示例来说明所获得结果的可行性和有效性。