Local and global exponential synchronization of complex delayed dynamical networks with general topology
Jin-Liang Wang Zhi-Chun Yang Tingwen Huang Mingqing Xiao
Discrete & Continuous Dynamical Systems - B 2011, 16(1): 393-408 doi: 10.3934/dcdsb.2011.16.393
In this paper, we consider a generalized complex network possessing general topology, in which the coupling may be nonlinear, time-varying, nonsymmetric and the elements of each node have different time-varying delays. Some criteria on local and global exponential synchronization are derived in form of linear matrix inequalities (LMIs) for the complex network by constructing suitable Lyapunov functionals. Our results show that the obtained sufficient conditions are less conservative than ones in previous publications. Finally, two numerical examples and their simulation results are given to illustrate the effectiveness of the derived results.
keywords: Complex networks time-varying delays exponential synchronization.
New passivity analysis of continuous-time recurrent neural networks with multiple discrete delays
Zhigang Zeng Tingwen Huang
Journal of Industrial & Management Optimization 2011, 7(2): 283-289 doi: 10.3934/jimo.2011.7.283
In this paper, by using some analytic techniques, several sufficient conditions are given to ensure the passivity of continuous-time recurrent neural networks with delays. The passivity conditions are presented in terms of some negative semi-definite matrices. They are easily verifiable and easier to check computing with some conditions in terms of complicated linear matrix inequality.
keywords: Passivity linear matrix inequality. neural networks negative semi-definite matrix delays
Study on self-adaptive proportional control method for a class of output models
Zhao-Han Sheng Tingwen Huang Jian-Guo Du Qiang Mei Hui Huang
Discrete & Continuous Dynamical Systems - B 2009, 11(2): 459-477 doi: 10.3934/dcdsb.2009.11.459
In this paper, self-adaptive proportional control method in economic chaotic system is discussed. It is not necessarily required for the fixed point having stable manifold in the method we used. One can stabilize chaos via time-dependent adjustments of control parameters; also can suppress chaos by adjusting external control signals. Two kinds of chaos about the output systems in duopoly are stabilized in a neighborhood of an unstable fixed point by using the chaos controlling method. The results show that performances of the system are improved by controlling chaos. Furthermore, their applications in practice are presented. The results also show that players can control chaos by adjusting their planned output or variable cost per unit according to the sign of marginal profit.
keywords: chaos control Duopoly games performance measure self-adaptive proportional control method
Synchronization of chaotic systems with time-varying coupling delays
Tingwen Huang Guanrong Chen Juergen Kurths
Discrete & Continuous Dynamical Systems - B 2011, 16(4): 1071-1082 doi: 10.3934/dcdsb.2011.16.1071
In this paper, we study the complete synchronization of a class of time-varying delayed coupled chaotic systems using feedback control. In terms of Linear Matrix Inequalities, a sufficient condition is obtained through using a Lyapunov-Krasovskii functional and differential equation inequalities. The conditions can be easily verified and implemented. We present two simulation examples to illustrate the effectiveness of the proposed method.
keywords: Chaotic System Synchronization Time-varying Delay.
2-D analysis based iterative learning control for linear discrete-time systems with time delay
Chuandong Li Fali Ma Tingwen Huang
Journal of Industrial & Management Optimization 2011, 7(1): 175-181 doi: 10.3934/jimo.2011.7.175
This paper investigates an iterative learning controller for linear discrete-time systems with state delay based on two-dimensional (2-D) system theory. It shall be shown that a 2-D linear discrete Roessor's model can be applied to describe the ILC process of linear discrete time-delay systems. Much less restrictive conditions for the convergence of the proposed learning rules are derived. A learning algorithm is presented which provides much more effective learning of control input, which enables us to obtain a control input to drive the system output to the desired trajectory quickly. Numerical examples are included to illustrate the performance of the proposed control procedures.
keywords: 2-D system theory Iterative learning control time delay. linear discrete system

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