scholarly journals Parameters Identification and Synchronization of Chaotic Delayed Systems Containing Uncertainties and Time-Varying Delay

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Zhongkui Sun ◽  
Xiaoli Yang
Keyword(s):  
Dynamical Systems ◽  
Functional Differential Equations ◽  
Parameters Identification ◽  
Time Varying ◽  
Unknown Parameters ◽  
Delayed Systems ◽  
Adaptive Scheme ◽  
Time Varying Delay ◽  
Functional Differential ◽  
Varying Delay

Time delays are ubiquitous in real world and are often sources of complex behaviors of dynamical systems. This paper addresses the problem of parameters identification and synchronization of uncertain chaotic delayed systems subject to time-varying delay. Firstly, a novel and systematic adaptive scheme of synchronization is proposed for delayed dynamical systems containing uncertainties based on Razumikhin condition and extended invariance principle for functional differential equations. Then, the proposed adaptive scheme is used to estimate the unknown parameters of nonlinear delayed systems from time series, and a sufficient condition is given by virtue of this scheme. The delayed system under consideration is a very generic one that includes almost all well-known delayed systems (neural network, complex networks, etc.). Two classical examples are used to demonstrate the effectiveness of the proposed adaptive scheme.

FURTHER RESULTS ON MASTER-SLAVE SYNCHRONIZATION OF GENERAL LUR'E SYSTEMS WITH TIME-VARYING DELAY

2008 ◽  
Vol 18 (01) ◽  
pp. 187-202 ◽  
Author(s):  
FERNANDO O. SOUZA ◽  
REINALDO M. PALHARES ◽  
EDUARDO M. A. M. MENDES ◽  
LEONARDO A. B. TÔRRES
Keyword(s):  
Communication Systems ◽  
Functional Differential Equations ◽  
Linear Matrix ◽  
Time Varying ◽  
Lur’E Systems ◽  
New Approach ◽  
Time Varying Delay ◽  
Delay Feedback Control ◽  
Functional Differential ◽  
Varying Delay

In this paper, a new approach to analyze the asymptotic, exponential and robust stability of the master-slave synchronization for Lur'e systems using time-varying delay feedback control is proposed. The discussion is motivated by the problem of transmitting information in optical communication systems using chaotic lasers. The approach is based on the Lyapunov–Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique with the use of a recent Leibniz–Newton model based transformation, without including any additional dynamics. Using the problem of synchronizing coupled Chua's circuits, three examples are given to illustrate the effectiveness of the proposed methodology.

scholarly journals Weak Projective Synchronization in Drive-Response Dynamical Networks with Time-Varying Delay and Parameter Mismatch

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jiang Xu ◽  
Song Zheng
Keyword(s):  
Impulsive Control ◽  
Functional Differential Equations ◽  
Projective Synchronization ◽  
Time Varying ◽  
Error Level ◽  
Parameter Mismatch ◽  
Dynamical Networks ◽  
Time Varying Delay ◽  
Functional Differential ◽  
Varying Delay

This paper investigates the problem of projective synchronization in drive-response dynamical networks (DRDNs) with time-varying delay and parameter mismatch via impulsive control. Owing to projective factor and parameter mismatch, complete projective synchronization cannot be achieved. Therefore, a weak projective synchronization scheme is proposed to ensure that the DRDNs are in a state of synchronization with an error level. Based on the stability analysis of the impulsive functional differential equations, a general method of the weak projective synchronization with the error level is derived in DRDNs. Numerical simulations are provided to verify the correctness and effectiveness of the proposed method and results.

scholarly journals New sufficient criteria for epsilon-contraction of a class of nonlinear diference system with continuous time

2020 ◽  
Vol 3 (3) ◽  
pp. 213-224
Author(s):  
Đặng Lệ Thuý ◽  
Cao Thanh Tinh ◽  
Lê Trung Hiếu ◽  
Lê Huỳnh Mỹ Vân
Keyword(s):  
Dynamical Systems ◽  
Continuous Time ◽  
Time Varying ◽  
Qualitative Properties ◽  
Practical Applications ◽  
Time Varying Delay ◽  
Difference Systems ◽  
Definition Of ◽  
Varying Delay ◽  
Delay Difference

Contraction property of dynamical systems, especially difference systems, is one of the qualitative properties which have attracted much attention from many researchers for recent decades. Contraction of dynamical systems has many practical applications which means that two trajectories of the system convergence to each other when the time reaches to positive infinity. In this paper, by improving some existing approaches, we present a new approach to contraction problem of a class of nonlinear time-varying delay difference system with continuous time. We generalize the definition of contraction to -contraction. Then, we give some new explicit sufficient criteria for -contraction and global exponential stability of the mentioned system. Furthermore, we investigate-contraction of perturbed difference systems with continuous time under nonlinear perturbations in which perturbations are general time-varying functions. Then we obtain a new explicit-contraction bound for such systems subject to nonlinear time-varying perturbations. The obtained theorems generalize some existing results in the literature as particular cases. An example is given to illustrate the obtained results.

New Stability Condition for Linear Systems with Time-Varying Delay

2014 ◽  
Vol 898 ◽  
pp. 843-846
Author(s):  
Li Jun Wang
Keyword(s):  
Stability Analysis ◽  
Positive Definite Matrix ◽  
Linear Matrix ◽  
Time Varying ◽  
Analysis Method ◽  
Delayed Systems ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Delay Dependent ◽  
Varying Delay

Generally, the obtained results on delayed systems can be classified into two types: delay-independent ones and delay-dependent ones. Delay-dependent stabilization problem for a class linear system with interval time-varying delay is studied. Early first proposed stability analysis method for systems with time-varying delay in a range, but the method therein still leaves much room for improvement. A sufficient condition in terms of linear matrix inequalities (LMIs) is achieved by constructing a novel Lyapunov-Krasovskii functional with the idea of partitioning the time delay, and then using free-weighting matrix approach and adopting inequalities, the interval delay is dealt with successfully. Compared with former stability analysis approaches, this approach can overcome the defect of finding a common positive definite matrix, and reduce conservative greatly. Finally, one simulation example is given to illustrate the effectiveness of the methods.

Robust sliding mode preview control for uncertain discrete-time systems with time-varying delay

2021 ◽  
pp. 095965182110553
Author(s):  
Junchao Ren ◽  
Changbin Jiang
Keyword(s):  
Sliding Mode ◽  
Reference Signal ◽  
Time Varying ◽  
Preview Control ◽  
Delayed Systems ◽  
Time Varying Delay ◽  
Sliding Motion ◽  
Small Gain ◽  
Time Systems ◽  
Varying Delay

This article focuses on the problem of robust sliding mode preview control for a class of non-linear delayed systems. It is assumed that the reference signal is previewed with a fixed length ahead and the norm of uncertainty is bounded. A model transformation is introduced to approximate the time-varying delay such that augmented error systems can be constructed. Conditions of asymptotic stability of sliding motion are established via the small gain theorem. The sliding mode preview controller is designed such that the controlled system state can be attracted to the switching surface and keep on it thereafter. A numerical example is presented to illustrate the effectiveness of the proposed control design.

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