Robust impulsive synchronization of complex delayed dynamical networks

Some Recent Advances in Complex Networks Synchronization

“…Now, consider the largest Lyapunov exponent L max of network (5). This L max is generally a function of the components and parameters of the network equation, such as f(·), A, Γ and c. This L max is usually referred to as the master stability function [20].…”

Drive network to a desired orbit by pinning control

“…, x in (t)) ∈ R n are the state variables of the ith dynamical node, f : R × R n × R n → R n is continuously vector-valued function governing the dynamics of isolated nodes, the time delay τ (t) may be unknown but is bounded by a known constant, i. e., 0 ≤ τ (t) ≤ τ , the positive constant c is the coupling strength, Γ(t) = (γ kl (t)) n×n ∈ R n×n is the inner-connecting matrix of the network at time t, B(t) = (b ij (t)) N ×N is the coupling configuration matrix representing the coupling strength and the topological structure of the network at time t, in which b ij (t) is defined as follows: If there is a connection from node i to node j (j = i) at time t, then b ij (t) = 0; otherwise, b ij (t) = 0 (j = i). Without loss of generality, we further assume that the coupling matrix B possesses the following properties [3,4,42]:…”

“…Next we consider an isolated dynamical node in the model (1), which is described by the following form of n-dimensional differential equations with time-varying delays [3]:…”

Finite-time synchronization of drive-response systems via periodically intermittent adaptive control

“…Many effective control methods including adaptive control [8][9][10][11][12][13][14], feedback control [15][16][17][18], observer control [19][20], pinning control [21][22][23], impulsive control [24][25][26][27][28] and intermittent control [29][30][31][32][33][34][35][36][37] have been proposed to drive the network to achieve synchronization. Among these control approaches, the discontinuous control methods which include impulsive control and intermittent control have attracted much interest due to its practical and easy implementation in engineering fields.…”