Abstract
•Markovian jumping complex dynamical networks with hybrid coupling and additive interval timevarying delay is considered.•We constructed the appropriate controllers to achieve impulsive and pinning control synchronization.•New delay-dependent impulsive and pinning control synchronization criteria are established.•Master-slave Markovian jumping complex dynamical networks are expressed as the error dynamical system.•LMI presented allow simultaneous computation of two bounds that characterize the synchronization rate.
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.