Exponential synchronization of nonlinearly coupled complex networks with hybrid time-varying delays via impulsive control

Abstract

This paper investigates the issue of exponential synchronization for a class of nonlinearly coupled complex networks with hybrid time-varying delays by applying impulsive control protocol. It should be mentioned we need not to assume the synchronization state since it may be difficult to find an appropriate function or dynamics to describe the synchronization manifold. By employing the Lyapunov method combined with average impulsive interval as well as the comparison principle, a set of simple and easily verifiable sufficient conditions are derived to guarantee the exponential synchronization for any initial values. Meanwhile, the exponential convergence rate can be specified through the analysis of the networks. Additionally, some numerical examples are given to verify the effectiveness of our theoretical results.

Pinning synchronization of complex delayed dynamical networks via generalized intermittent adaptive control strategy

“…For the sake of driving the networks to achieve synchronization, the proper controllers are designed. Up to now, many typical and useful control methods have been proposed, such as adaptive control, feedback control, pinning control, intermittent control, event‐triggered control, and impulsive control …”

“…Up to now, many typical and useful control methods have been proposed, such as adaptive control, 9,10 feedback control, 11,12 pinning control, 13,14 intermittent control, 15,16 event-triggered control, 17,18 and impulsive control. 19,20 Recently, as discontinuous control approach, intermittent control has attracted increasing interest naturally in a variety of applications because this control method is more economic and can reduce the amount of the transmitted information. In practice, intermittent control scheme is composed of control time and the rest time in turn.…”

Synchronization in nonlinear complex networks with multiple time‐varying delays via adaptive aperiodically intermittent control

“…[34][35][36][37] In particular, intermittent control, as a discontinuous control strategy, is more economical and has been adopted to design controllers for synchronization. [34][35][36][37] In particular, intermittent control, as a discontinuous control strategy, is more economical and has been adopted to design controllers for synchronization.…”

“…In general, complex networks are difficult to synchronize by themselves, and many control technologies such as sliding-mode control, impulsive control, intermittent control, and some hybrid control methods were introduced to actuate networks to the objective states. [34][35][36][37] In particular, intermittent control, as a discontinuous control strategy, is more economical and has been adopted to design controllers for synchronization. In the work of Ma and Wang, 38 by using periodically pinning intermittent control, some synchronization criteria were derived for delayed networks; in the work of Liang and Wang, 39 the authors studied the synchronization problems in virtue of intermittent control with two switched periods; in a further step, intermittent control with multiple switched periods was also extended.…”

Finite/fixed-time synchronization for complex networks via quantized adaptive control

“…Synchronization, which means that all dynamic nodes tend common dynamic behavior, is a typical dynamic phenomenon in complex networks. In recent years, various synchronization control strategies have been provided, which mainly include impulsive control [7], adaptive control [5,12], sliding mode control [10], periodic intermittent control [18], and pinning control [20] etc.…”