Lag and anticipatory synchronization based parameter estimation scheme in modulated time-delayed systems

In this article, we have shown that using delay dynamical systems as base, one can use the modulation of the various parameters, to transmit multiple signals through a single chaotic time series. It is shown that under certain conditions the original signals and parameters of the driving signals can be recovered with the help of an adaptive demodulator. An important aspect of the present method is that the communication is possible between two time-delayed systems with parameter mismatch using lag and anticipatory synchronization. The whole idea is presented on the basis of Mackey–Glass system, with variable time delay.     

Exponential stability criterion for time-delay systems with nonlinear uncertainties

Exponential stability of time-delay systems with nonlinear uncertainties is studied in this paper. Based on the Lyapunov method and the approaches of decomposing the matrix, a new exponential stability criterion is derived in terms of a matrix inequality, which allows to compute simultaneously the two bounds that characterize the exponential nature of the solution. Some numerical examples are also given to show the superiority of our result to those in the literature.     

Exponential stability analysis and impulsive tracking control of uncertain time-delayed systems

In this paper, we study exponential stability and tracking control problems for uncertain time-delayed systems. First, sufficient conditions of exponential stability for a class of uncertain time-delayed systems are established by employing Lyapunov functional methods and algebraic matrix inequality techniques. Furthermore, tracking control problems are investigated in which an uncertain linear time-delayed system is used to track the reference system. Sufficient conditions for solvability of tracking control problems are obtained for the cases that the system state is measurable and non-measurable, respectively. When the state is measurable, we design an impulsive control law to achieve the tracking performance. When the state information is not directly available from measurement, an impulsive control law based on the measured output will be used. Finally, numerical examples are presented to illustrate the effectiveness and usefulness of our results.     

Complex synchronization manifold in coupled time-delayed systems

In the present paper, the complex synchronization manifold generated in coupled multiple time delay systems is demonstrated for the first time. There, the manifold is in the form of sum of multiple simple manifolds. The structure of master is identical to that of slave. The equation for driving signal is the sum of nonlinearly transformed components of delayed state variable. The specific examples will demonstrate and verify the effectiveness of the proposed model.     

Generalized projective synchronization in time-delayed chaotic systems

We report on generalized projective synchronization between two identical time delay chaotic systems with single time delays. It overcomes some limitations of the previous work where generalized projective synchronization has been investigated only in finite-dimensional chaotic systems, so we can achieve generalized projective synchronization in infinite-dimensional chaotic systems. This method allows us to arbitrarily direct the scaling factor onto a desired value. Numerical simulations show that this method works very well.     

Fuzzy delayed output feedback synchronization for time-delayed chaotic systems

In this paper, we propose a new fuzzy delayed output feedback synchronization (FDOFS) method for time-delayed chaotic systems. Based on Lyapunov–Krasovskii theory, T–S fuzzy model, and delayed feedback control scheme, the FDOFS controller is designed and an analytic expression of the controller is shown. The proposed controller can guarantee asymptotical synchronization of both drive and response systems. The FDOFS controller can be obtained by solving the linear matrix inequality (LMI) problem. A numerical example for time-delayed Lorenz system is presented to demonstrate the validity of the proposed FDOFS method.     

Parametric generation of robust chaos with time-delayed feedback and modulated pump source

We consider a chaos generator composed of two parametrically coupled oscillators whose natural frequencies differ by factor of two. The system is driven by modulated pump source on the third harmonic of the basic frequency, and on each next period of pumping the excitation of the oscillator of doubled frequency is stimulated by the signal from the oscillator of the basic frequency undergoing quadratic nonlinear transformation and time delay. Using qualitative analysis and numerical results, we argue that chaotic dynamics in the system corresponds to hyperbolic strange attractor. It is a kind of Smale–Williams solenoid embedded in the infinite-dimensional state space of the stroboscopic map of the time-delayed system.     

Global impulsive exponential synchronization of time-delayed coupled chaotic systems

In this paper, the impulsive exponential synchronization problem for time-delayed coupled chaotic systems is investigated. By establishing an impulsive differential delay inequality and using the property of P-cone, some simple conditions of impulsive exponential synchronization of two coupled chaotic systems are derived. To illustrate the effectiveness of the new scheme, some numerical examples are given.     

A simple global synchronization criterion for coupled chaotic systems

Based on the Lyapunov stabilization theory and Gerschgorin theorem, a simple generic criterion is derived for global synchronization of two coupled chaotic systems with a unidirectional linear error feedback coupling. This simple criterion is applicable to a large class of chaotic systems, where only a few algebraic inequalities are involved. To demonstrate the efficiency of design, the suggested approach is applied to some typical chaotic systems with different types of nonlinearities, such as the original Chua’s circuit, the modified Chua’s circuit with a sine function, and the Rössler chaotic system. It is proved that these synchronizations are ensured by suitably designing the coupling parameters.     

Chaos and chaos synchronization for a non-autonomous rotational machine systems

Chaos and chaos synchronization of the centrifugal flywheel governor system are studied in this paper. By mechanics analyzing, the dynamical equation of the centrifugal flywheel governor system is established. Because of the non-linear terms of the system, the system exhibits both regular and chaotic motions. The characteristic of chaotic attractors of the system is presented by the phase portraits and power spectra. The evolution from Hopf bifurcation to chaos is shown by the bifurcation diagrams and a series of Poincaré sections under different sets of system parameters, and the bifurcation diagrams are verified by the related Lyapunov exponent spectra. This letter addresses control for the chaos synchronization of feedback control laws in two coupled non-autonomous chaotic systems with three different coupling terms, which is demonstrated and verified by Lyapunov exponent spectra and phase portraits. Finally, numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.     

Universal chaos synchronization control laws for general quadratic discrete systems

This paper addresses the reliable universal synchronization problem between two coupled chaotic quadratic discrete systems. A general nonlinear control method of synchronization for coupled 2D and 3D quadratic dynamical systems in discrete-time is proposed. The proposed synchronization method is based on universal controllers. The synchronization results are derived theoretically using active control method and Lyapunov stability theory. Numerical simulations are performed to assess the performance of the presented analysis.     

Exponential synchronization between two classes of chaotic systems

In this paper, the concept of exponential synchronization is introduced and the chaos synchronization between uncertain Genesion system and Rossler system is investigated. Based on the time-domain approach, a tracking control is proposed such that uncertain Genesion system exponentially synchronizes the Rossler system with any pre-specified exponential convergence rate. Finally, a numerical example is provided to illustrate the use of the main results.     

Stability criterion for synchronization of linearly coupled unified chaotic systems

This paper investigates the synchronization of two linearly coupled unified chaotic systems. A new stability criterion for asymptotic synchronization is attained using the Lyapunov stability theory and linear matrix inequality (LMI) approach. A numerical example is given to illuminate the design procedure and advantage of the result derived.     

Observer-based adaptive control of chaos in nonlinear discrete-time systems using time-delayed state feedback

A new approach to adaptive control of chaos in a class of nonlinear discrete-time-varying systems, using a delayed state feedback scheme, is presented. It is discussed that such systems can show chaotic behavior as their parameters change. A strategy is employed for on-line calculation of the Lyapunov exponents that will be used within an adaptive scheme that decides on the control effort to suppress the chaotic behavior once detected. The scheme is further augmented with a nonlinear observer for estimation of the states that are required by the controller but are hard to measure. Simulation results for chaotic control problem of Jin map are provided to show the effectiveness of the proposed scheme.     

A new stability criterion for linear discrete systems

This paper is concerned with the stability of difference equations. A criterion to decide whether a certain polynomial has all its zeros inside the unit circle is applied to multistep linear methods in order to obtain the absolute stability region, and it is shown how this region can be extended. Systems of linear difference equations are also considered and an extension to partial difference equations is discussed.     

Sufficient and necessary conditions for absolute stability of time-delayed Lurie control systems

In this paper, we present some sufficient and necessary conditions for the absolute stability of time-delayed Lurie control systems, which improve the results we obtained before for the absolute stability of direct control, indirect control and critical control of Lurie systems. We also derived certain simple and easy applicable algebraic sufficient conditions for the absolute stability of time-delayed Lurie control systems, which provide a convenient tool for practical control engineers in designing absolutely stable systems or stabilizing nonlinear control systems.     

Exponential stability and estimates for monotone and differential-difference systems

We present necessary and sufficient conditions for the exponential stability in the nonnegative cone and refine exponential estimates for solutions of systems of autonomous difference equations with monotone nondecreasing right-hand sides, including discontinuous ones, as well as for solutions of some class of systems of differential-difference equations with monotonicity. Unlike well-known criteria, the new ones are free of some additional assumptions on the right-hand sides of the considered models other than the original monotonicity conditions. We show that, in the nonsmooth and discontinuous cases, the traditional exponential stability conditions based on ??linearization?? can lead to negative or very coarse results.     

Exponential synchronization for fractional‐order chaotic systems with mixed uncertainties

This article focuses on the problem of exponential synchronization for fractional‐order chaotic systems via a nonfragile controller. A criterion for α‐exponential stability of an error system is obtained using the drive‐response synchronization concept together with the Lyapunov stability theory and linear matrix inequalities approach. The uncertainty in system is considered with polytopic form together with structured form. The sufficient conditions are derived for two kinds of structured uncertainty, namely, (1) norm bounded one and (2) linear fractional transformation one. Finally, numerical examples are presented by taking the fractional‐order chaotic Lorenz system and fractional‐order chaotic Newton–Leipnik system to illustrate the applicability of the obtained theory. © 2014 Wiley Periodicals, Inc. Complexity 21: 114–125, 2015