Exponential Synchronization of Neural Networks via Feedback Control in Complex Environment

Abstract

The problem of exponential synchronization for neural networks is investigated via feedback control in complex environment. By constructing suitable Lyapunov-Krasovskii functionals and applying the piecewise analytic method, some sufficient criteria for exponential synchronization of the addressed neural networks are established in terms of linear matrix inequalities (LMIs). The feedback control in complex environment includes the delayed aperiodically intermittent control and dynamic output feedback control. Moreover, the delayed aperiodically intermittent dynamic output feedback controller is designed based on the established LMIs. A numerical example and its numerical simulations are finally presented to show the effectiveness of obtained theoretical results.

Synchronization Analysis of Complex Dynamical Networks Subject to Delayed Impulsive Disturbances

“…Considering the feedback control involving impulsive disturbances into account, one can see that synchronization is achieved with a fast rate of convergence, see Figures 7(a)-7(d). Note that those synchronization criteria in [14,18,19,31] are infeasible for the abovementioned example due to the existence of delayed impulsive disturbance. Here, our proposed Complexity theoretical result has wider applications than those existing results.…”

“…As a type of complex networks, coupled neural networks have received great attention and a lot of previous studies mainly focused on stability and stabilization analysis [9][10][11][12][13]. Since synchronization is a widespread collective behavior in nature that has been broadly used in various domains, such as information science, signal processing, and communication system [14][15][16][17][18][19][20]. More and more investigators devote to investigating the various types of synchronization of complex networks: phase synchronization [21], complete synchronization [22], and cluster synchronization [23].…”

Stability of delay neural networks with uncertainties via delayed intermittent control

“…Neural networks (NNs) have been widely investigated recently because of their potential applications in many areas such as associative memory, pattern recognition, parallel computing, and image processing; see [1][2][3][4][5][6][7] and references therein. In these real applications, stability property of equilibrium points of the networks is an important factor in the design of NNs.…”

Parameter Identification and Adaptive Control of Uncertain Goodwin Oscillator Networks with Disturbances

“…From the viewpoint of mathematics, the core of synchronization is the stability of the zero solution of network error systems [14][15][16]. In previous studies, two effective methods are usually employed: the first one is to study synchronization induced by the mutual couplings between nodes [17,18], and the second one is to design reasonable control laws [19][20][21]. A great number of researches on the first method have indicated that synchronization without external control needs certain requirement in both network structures and node dynamics.…”