Pinning Impulsive Stabilization of Nonlinear Dynamical Networks With Time-Varying Delay

Abstract

In this paper, a new impulsive control strategy, namely pinning impulsive control, is proposed for the stabilization problem of nonlinear dynamical networks with time-varying delay. In this strategy, only a small fraction of nodes is impulsively controlled to globally exponentially stabilize the whole dynamical network. By employing the Lyapunov method combined with the mathematical analysis approach as well as the comparison principle for impulsive systems, some criteria are obtained to guarantee the success of the global exponential stabilization process. The obtained criteria are closely related to the proportion of the controlled nodes, the impulsive strength, the impulsive interval and the time-delay. Numerical examples are given to demonstrate the effectiveness of the designed pinning impulsive controllers.

Adaptive exponential lag synchronization for neural networks with mixed delays via intermittent control

“…In order to guarantee synchronization between two chaotic systems can be realized, several control schemes have been proposed, such as feedback control, adaptive control, intermittent control and impulsive control [12][13][14][15][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. Intermittent control, as a discontinuous control method, has been adopted in engineering fields in view of its convenient implementation in engineering control [33][34][35][36][37][38].…”

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

“…Various control schemes have been used to study the synchronization problems, and typical control methods include pinning control [7][8][9], adaptive control [10,11] and impulsive control [12][13][14][15][16]. Especially, impulsive control has captured a lot of researchers' attentions because of its applications in many areas such as orbital transfer of satellite, ecosystems management and chaos synchronization for secure communication.…”

“…Furthermore, using impulsive control, a new approach for analyzing pinning stability in a complex dynamical network was proposed [14]. In additional, Lu et al [15] investigated the stabilization problem of nonlinear dynamical networks with time-varying delay by pinning impulsive control. Very recently, Cai et al introduced two types of impulses to analyze the synchronization of directed complex networks with timedelayed dynamical nodes in [16].…”

“…There generally exist two types of time delay in dynamical networks: one is internal delay occurring inside the dynamical node [17][18][19][20], and the other is coupling delay caused by the exchange of information between dynamical nodes [8,15,[21][22][23][24]. Therefore, realistic modeling of dynamical networks should require both of them to be taken into account.…”

Drive network to a desired orbit by pinning control

“…And later on, Yu et al [36] concerned with pinning performance of complex dynamical network. Other research works about pinning control of complex networks can be seen in [8,12,17,22,23,24,26,30,31,32,33,34,35,40,41] and many references cited therein.…”