Robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties

Abstract

The problem of robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties is investigated in this article. It is only assumed that the upper normal bound of uncertain inner and outer coupling matrices is positive but its concrete structure is not also required to be known. The time‐varying coupling delay is a any nonnegative continuous and bounded function and not require its derivative to be less than one, that is, general time‐varying coupling delays and uncertainties. For such a class of uncertain complex networks, a new synchronization scheme is presented by a class of continuous memoryless robust decentralized adaptive synchronization controllers. It is also shown that the synchronization error dynamics of uncertain complex networks can be guaranteed as uniformly exponentially convergent toward a ball that can be as small as desired. Finally, numerical simulations are provided to demonstrate the effectiveness and robustness of proposed complex networks synchronization schemes. © 2013 Wiley Periodicals, Inc. Complexity 19: 10–26, 2014

Chaos control of uncertain time‐delay chaotic systems with input dead‐zone nonlinearity

“…Thus, it follows that the existence of R, P, and K satisfying the condition (5) is equivalent to the existence of M, X , and W satisfying the LMI condition (10). By Theorem 1, the existence of M, X , and W satisfying the LMI condition (10) guarantees the uncertain time-delay chaotic system with input deadzone nonlinearity (3) in the sliding mode is asymptotically stable.…”

“…The prominent characteristic of a chaotic system is its extreme sensitivity to initial conditions and the system's parameters. Over the past decades, chaos control has been widely investigated and many researches have been studied in this field [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. In [1], a linear feedback control method is proposed for controlling uncertain L€ u system.…”

“…yield the matrix inequality (10). Thus, it follows that the existence of R, P, and K satisfying the condition (5) is equivalent to the existence of M, X , and W satisfying the LMI condition (10).…”

Projective Exponential Synchronization for a Class of Complex PDDE Networks with Multiple Time Delays

“…Time delays may cause bifurcation, oscillation, divergence or instability of complex networks [15][16][17]. Thus, it is extremely important to study the dynamics of complex networks considering time delays, which has become a hotly discussed issue in the area of complex networks studies [18][19][20][21][22][23]. In addition, a kind of complex networks called complex spatiotemporal networks (e.g., biological systems [24]) have also attracted researchers' attention in the past few years.…”

Single state feedback stabilization of unified chaotic systems and circuit implementation

“…For this reason, designing simple and available control input is extremely relevant for experimental chaos control. Besides the OGY method, many other control algorithms have been proposed in recent years to control chaotic systems, such as PC method [9][10][11], feedback approach [12,13], adaptive control [14][15][16], linear state space feedback [17], backstepping method [18], nonlinear feedback control [19], sliding mode control [20,21], neural network control [22], fuzzy logic control [23], robust control [24][25][26][27][28][29][30], passivity theory control [31], adaptive passive control [32], time-delay feedback approach [33,34], multiple delay feedback control [35], double delayed feedback control [36], hybrid control [37], etc. These control algorithms can be used to stabilize a desired unstable periodic orbit (UPO) embedded within a chaotic attractor.…”