Feedback control based on discrete-time state observations on synchronization of stochastic impulsive coupled systems

In this paper, feedback control based on discrete-time state observations is used to study the inner synchronization of stochastic impulsive coupled systems (SICSs). Therein, the coupling strength of SICSs is state-dependent switching and time-varying under each switching. Besides, by means of average impulsive interval approach, the Lyapunov method and the graph theory, a synchronization criterion of SICSs is presented. As an application, stochastic impulsive coupled Chua’s circuits with state-dependent switching coupling strength are investigated for the first time and some sufficient conditions are given. Finally, in order to illustrate the effectiveness of our main results, some numerical simulations are presented.     

Finite-time synchronization for coupled systems with time delay and stochastic disturbance under feedback control

This paper proposes a framework for finite-time synchronization of coupled systems with time delay and stochastic disturbance under feedback control. Combining Kirchhoff"s Matrix Tree Theorem with Lyapunov method as well as stochastic analysis techniques, several sufficient conditions are derived. Differing from previous references, the finite time provided by us is related to topological structure of networks. In addition, two concrete applications about stochastic coupled oscillators with time delay and stochastic Lorenz chaotic coupled systems with time delay are presented, respectively. Besides, two synchronization criteria are provided. Ultimately, two numerical examples are given to illustrate the effectiveness and feasibility of the obtained results.     

Stabilization problem of stochastic time-varying coupled systems with time delay and feedback control

The stabilization of stochastic coupled systems with time delay and time-varying coupling structure (SCSTT) via feedback control is investigated. We generalize systems with constant coupling structure to the time-varying coupling structure. Combining the graph theory with the Lyapunov method, a systematic method is provided to construct a Lyapunov function for SCSTT, and a Lyapunov-type theorem and a coefficient-type criterion are obtained to guarantee the stabilization in the sense of pth moment exponential stability. Furthermore, theoretical results are applied to analyze the stabilization of stochastic-coupled oscillators with time delay and time-varying coupling structure in order to illustrate the practicability of the results. Finally, two numerical examples are given to illustrate the effectiveness and feasibility of theoretical results.     

Synchronization of quaternion-valued coupled systems with time-varying coupling via event-triggered impulsive control

In this paper, the problem of exponential synchronization of quaternion-valued coupled systems based on event-triggered impulsive control is investigated for the first time. It should be pointed out that the coupling strength is quaternion-valued and time-varying, which makes our model more in line with practical models. First, we prove that event-triggered impulsive control can exclude Zeno behavior. Then, based on the Lyapunov method and the graph theory, some sufficient conditions are derived to ensure that quaternion-valued coupled systems reach synchronization. Furthermore, as an application of our theoretical results, exponential synchronization of quaternion-valued Kuramoto oscillators is studied in detail and a synchronization criterion is presented. Finally, some numerical simulations are given to show the effectiveness of our theoretical results.     

Exponential synchronization of stochastic coupled oscillators networks with delays

This paper investigates the exponential synchronization problem of coupled oscillators networks with disturbances and time-varying delays. On basis of graph theory and stochastic analysis theory, a feedback control law is designed to achieve exponential synchronization. By constructing a global Lyapunov function for error network, both pth moment exponential synchronization and almost sure exponential synchronization of drive-response networks are obtained. Finally, a numerical example is given to show the effectiveness of the proposed criteria.     

Synchronization of a chaotic electronic circuit system with cubic term via adaptive feedback control

This paper presents an adaptive feedback control scheme for the synchronization of the chaotic system consisting of Van der Pol oscillators coupled to linear oscillators with cubic term when the parameters of the master system are unknown and different with the those of the slave system. Based on the Lyapunov stability theory, an adaptive control law is derived to make the states of two slightly mismatched chaotic systems asymptotically synchronized. This method is efficient and easy to implement. Numerical simulations results confirming the analytical predictions are shown and pspice simulations are also performed to confirm the efficiency of the proposed control 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.     

Synchronization for the coupled stochastic strict-feedback nonlinear systems with delays under pinning control

In this paper, a class of new coupled stochastic strict-feedback nonlinear systems with delays (CSFND) on networks without strong connectedness (NWSC) is considered, and the issue pertaining to the synchronization of the systems is discussed by pinning control. Towards CSFND, the controllers are approached by combining the back-stepping method and the design of virtual controllers. A key novel design ingredient is that the global Lyapunov function is obtained based on each Lyapunov function of stochastic strict-feedback nonlinear systems with delays (SFND). Moreover, a sufficient criterion is presented to realize the exponential synchronization by employing the graph theory and Lyapunov method. As a subsequent result, we apply the obtained theoretical results to the second-order oscillator systems and robotic arm systems. Meanwhile, numerical simulations are provided to demonstrate the validity and feasibility of our theoretical results.     

Synchronized stationary distribution of stochastic coupled systems based on graph theory

This paper deals with the synchronized stationary distribution of stochastic coupled systems. The response system is constructed to help achieve a synchronized stationary distribution. Firstly, an error system obtained by the drive system and the response system is given and an appropriate Lyapunov function for the error system is constructed. On the basis of the graph theory and the Lyapunov method, some sufficient conditions are proposed to guarantee the existence of a stationary distribution for the error system, which reflects the coupling structure has a close relationship with synchronized stationary distribution. Then, an application to stochastic coupled oscillators is presented and sufficient conditions are obtained to illustrate the feasibility of the theoretical results. Finally, a numerical example is provided to demonstrate the effectiveness of theoretical results.     

LMI Optimization Approach to Synchronization of Stochastic Delayed Discrete-Time Complex Networks

Complex networks are widespread in real-world systems of engineering, physics, biology, and sociology. This paper is concerned with the problem of synchronization for stochastic discrete-time drive-response networks. A dynamic feedback controller has been proposed to achieve the goal of the paper. Then, based on the Lyapunov second method and LMI (linear matrix inequality) optimization approach, a delay-independent stability criterion is established that guarantees the asymptotical mean-square synchronization of two identical delayed networks with stochastic disturbances. The criterion is expressed in terms of LMIs, which can be easily solved by various convex optimization algorithms. Finally, two numerical examples are given to illustrate the proposed method.     

Chaotic synchronization by the intermittent feedback method

This paper studies the synchronization of chaotic systems by the intermittent feedback method which is efficient. A sufficient synchronization criterion for a general intermittent linear state error feedback control is obtained by using a Lyapunov function and differential inequalities. Numerical simulations for the chaotic Chua oscillator are presented to illustrate the theoretical results.     

Finite-time dissipative control for singular discrete-time Markovian jump systems with actuator saturation and partly unknown transition rates

In this work, the finite-time dissipative control problem is considered for singular discrete-time Markovian jumping systems with actuator saturation and partly unknown transition rates. By constructing a proper Lyapunov–Krasonski functional and the method of linear matrix inequalities (LMIs), sufficient conditions that ensure the systems singular stochastic finite-time stability and singular stochastic finite-time dissipative are obtained. Then, the state feedback controllers are designed, and in order to get the optimal values of the dissipative level, the results are extended to LMI convex optimization problems. Finally, numerical examples are given to illustrate the validity of the proposed methods.     

ADAPTIVE PINNING SYNCHRONIZATION OF COUPLED NEURAL NETWORKS WITH MIXED DELAYS AND VECTOR-FORM STOCHASTIC PERTURBATIONS＊

In this article,we consider the global chaotic synchronization of general coupled neural networks,in which subsystems have both discrete and distributed delays.Stochastic perturbations between subsyste...     

Synchronization for stochastic hybrid coupled controlled systems with Lévy noise

In this paper, synchronization for stochastic hybrid-delayed coupled systems with Lévy noise on a network (SHDCLN) is investigated via aperiodically intermittent control. Here time delays, Markovian switching and Lévy noise are considered on a network simultaneously for the first time. After that, by means of Lyapunov method, graph theory, and some techniques of inequality, some sufficient conditions are derived to guarantee the synchronization for SHDCLN. In addition, the designed range of aperiodically intermittent controller parameters is shown. Meanwhile, the coupling strength and the perturbed intensity of noise have a great impact on the intensity of control. Then, we investigate synchronization for stochastic hybrid delayed Chua's circuits with Lévy noise on a network as a practical application of our theoretical results. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.     

Chaos synchronization for a class of nonlinear oscillators with fractional order

In this paper, a special kind of nonlinear chaotic oscillator, the Qi oscillator, is studied in detail. Since such systems are shown to possess a relatively wide spectral bandwidth, it is considerably beneficial to practical engineering in the secure communication field. The chaos synchronization problem of the fractional-order Qi oscillators coupled in a master-slave pattern is examined by applying three different kinds of methods: the nonlinear feedback method, the one-way coupling method and the method based on the state observer. Suitable synchronization conditions are derived by using the Lyapunov stability theory, and most importantly, a sufficient and necessary synchronization condition for the case with fractional order between 1 and 2 is presented. Results of numerical simulations validate the effectiveness and applicability of the proposed schemes.     

$H_{\infty}$ feedback controls based on discrete-time state observations for singular hybrid systems with nonhomogeneous Markovian jump

In this paper, the $H_{\infty}$-control problem for singular Markovian jump systems (SMJSs) with variable transition rates by feedback controls based on discrete-time state observations is studied. The mode-dependent time-varying character of transition rates is supposed to be piecewise-constant. By designing a feedback controller based on discrete-time state observations, employing a stochastic Lyapunov-Krasovskii functional, and combining with the linear matrix inequalities (LMIs) technologies, sufficient conditions under the case of nonhomogeneous transition rates are developed such that the controlled system is regular, impulse free, and stochastically stable. Subsequently, the upper bound on the duration $\tau$ between two consecutive state observations and prescribed $H_{\infty}$ performance $\gamma$ are derived. Moreover, the achieved results can be easily checked by the Matlab LMI Tool Box. Finally, two numerical examples are presented to show the effectiveness of the proposed methods.     

A graph‐theoretic approach to stability of neutral stochastic coupled oscillators network with time‐varying delayed coupling

In this paper, a graph‐theoretic approach for checking exponential stability of the system described by neutral stochastic coupled oscillators network with time‐varying delayed coupling is obtained. Based on graph theory and Lyapunov stability theory, delay‐dependent criteria are deduced to ensure moment exponential stability and almost sure exponential stability of the addressed system, respectively. These criteria can show how coupling topology, time delays, and stochastic perturbations affect exponential stability of such oscillators network. This method may also be applied to other neutral stochastic coupled systems with time delays. Finally, numerical simulations are presented to show the effectiveness of theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.     

Anticipating synchronization through optimal feedback control

In this paper, we investigate the anticipating synchronization of a class of coupled chaotic systems through discontinuous feedback control. The stability criteria for the involved error dynamical system are obtained by means of model transformation incorporated with Lyapunov functional and linear matrix inequality. Also, we discuss the optimal designed controller based on the obtained criteria. The numerical simulation is presented to demonstrate the theoretical results.     

Finite‐time synchronization of a class of N‐coupled complex partial differential systems with time‐varying delay

This study examines finite‐time synchronization for a class of N‐coupled complex partial differential systems (PDSs) with time‐varying delay. The problem of finite‐time synchronization for coupled drive‐response PDSs with time‐varying delay is similarly considered. The synchronization error dynamic of the PDSs is defined in the q‐dimensional spatial domain. We construct a feedback controller to achieve finite‐time synchronization. Sufficient conditions are derived by using the Lyapunov‐Krasoviskii stability approach and inequalities technology to ensure that the proposed networks achieve synchronization in finite time. The proposed systems demonstrate extensive application. Finally, an example is used to verify the theoretical results.     

Finite-time stabilization of state dependent impulsive dynamical linear systems

The problem of finite-time stabilizing control design for state-dependent impulsive dynamical linear systems (SD-IDLS) is tackled in this paper. Such systems are characterized by continuous-time, linear, possibly time-varying, dynamics coupled with discrete-time, linear, possibly time-varying, dynamics. The continuous-time part determines the system evolution in any time interval between two consecutive resetting events, while the discrete-time part governs its instantaneous state jump whenever the system trajectory intersects a resetting set, i.e. a region of the state space assumed to be time-independent. By making use of a quadratic control Lyapunov function, the finite-time stabilization of SD-IDLS through a static output feedback control design is specifically discussed in this paper. A sufficient and constructive result is provided based on the conical hulls of the resetting set subregions and on some cone copositivity properties of the chosen control Lyapunov function. Such a result is based on the solution of a feasibility problem that involves a set of coupled Difference/Differential Linear Matrix Inequalities (D/DLMI), which is shown to be less conservative and more numerically amenable with respect to other results available in the literature. An example illustrates the effectiveness of the proposed approach.