Fault-Tolerant Master–Slave Synchronization for Lur'e Systems Using Time-Delay Feedback Control

This paper deals with fault-tolerant master–slave synchronization for Lur'e systems using time-delay feedback control. Taking a general nature of fault in the master system into account, a new synchronization scheme, namely, fault-tolerant master–slave synchronization, is proposed, by which the master–slave synchronization can be achieved no matter if the fault occurs or not. By making use of an observer-based fault estimator and a modified time-delay feedback controller, the fault-tolerant master–slave synchronization is formulated so as to discuss the global asymptotic stability of the error system and the bound of energy gain from fault to state and fault estimation error vectors. Some new delay-dependent criteria are derived to analyze the synchronization error system, and based on the analysis results, a sufficient condition on the existence of such a master–slave synchronization scheme and a solution to the controller and fault-estimator gain matrices are obtained in terms of linear matrix inequalities. Finally, a Chua's circuit is used to illustrate the effectiveness of the proposed method.      

Adaptive Stabilization and Synchronization for Chaotic Lur'e Systems With Time-Varying Delay

In this paper, we propose an adaptive scheme for the stabilization and synchronization of chaotic Lur'e systems with time-varying delay. Based on the invariant principle of functional differential equations, the strength of the feedback controller is enhanced adaptively to stabilize and synchronize chaotic Lur'e systems. The derivative-constraint that the time-varying delay is required to be differentiable and its derivation is less than one can be removed by using LaSalle-Razumikhin-type theorems. The time-varying delay is allowed to be bounded without any additional constraint or unbounded with derivative-constraint. This method is analytical, rigorous and simple to implement in practice. In addition, it is quite robust against the effect of parameters uncertainty and noise. Two examples are provided to show the effectiveness of the proposed scheme. The results of the paper demonstrate the fruitfulness of the modern feedback and adaptive control theory application to the stabilization and synchronization problems for delayed chaotic systems.     

Impulsive Synchronization of Chaotic Lur'e Systems by Linear Static Measurement Feedback: An LMI Approach

In this brief, we consider impulsive control for master-slave synchronization schemes that consist of identical chaotic Lur'e systems. Impulsive control laws are investigated which make use of linear static measurement feedback, instead of full state feedback. A less conservative sufficient condition than existing results for global asymptotic impulsive synchronization is presented, in which synchronization is proven for the error between the full state vectors. And then an linear matrix inequality (LMI)-based approach for designing linear static output feedback impulsive control laws to globally asymptotically synchronize Lur'e chaotic systems is derived. With the help of the LMI solvers, we can easily obtain the linear output feedback impulsive controller and the bound of the impulsive interval for global asymptotic synchronization. The method is illustrated on Chua's circuit.     

On Synchronization Errors in Networked Feedback Systems

This paper addresses the problem of synchronization errors and their effects on feedback loops that are closed over communication networks. It is assumed that the feedback loop consists of two discrete-time systems, the clock frequency ratio of which has a special rational form, and is close to one. A Toeplitz matrix approach is taken to model the input/output relationship of the arising feedback systems. Based on this representation, the effect of synchronization errors on stability of the feedback systems is analyzed. It is shown that stability of the synchronized feedback loop can not guarantee stability of the loop in the presence of synchronization errors. Necessary and sufficient stability conditions are derived.     

Improved Global Asymptotical Synchronization of Chaotic Lur'e Systems With Sampled-Data Control

This brief investigates the global asymptotical synchronization problem of chaotic Lur'e systems with sampled-data control. Based on a time-varying delay system transformed from the sampled-data error system, an augmented Lyapunov functional containing some useful system information is constructed, no useful terms in the derivative of the Lyapunov functional are ignored, and the relationship among the time-varying delay, its upper bound, and their difference is taken into account. A less conservative delay-dependent synchronization criterion expressed in terms of linear matrix inequalities is obtained. The effectiveness and merits of the proposed method are finally illustrated via numerical simulations for Chua's circuits.     

区间时变时滞系统的时滞相关稳定性分析

研究了具有区间时变时滞线性不确定系统的稳定性问题。通过引入新型的Lyapunov泛函,结合改进型的Jensen积分不等式,推导出区间时变时滞线性系统的时滞相关鲁棒稳定新判据。该方法在推导过程中没有用到模型变换及自由权矩阵方法,简化了计算上的复杂性。由于判据中充分利用了时变时滞的中值及时滞变化范围两个参数,减少了结果的保守性。数值算例表明了提出方法的有效性及优越性。     

Exponential Stability Criteria for Positive Systems with Time-Varying Delay: A Delay Decomposition Technique

This paper is concerned with exponential stability analysis for linear continuous positive systems with bounded time-varying delay. Our approach is based on Lyapunov–Krasovskii functional with delay decomposition. The main idea is to divide uniformly the discrete delay interval into multiple segments and then to choose proper functionals with different weighted matrices corresponding to different segments. The synthesis of our delay-dependent sufficient stability criteria is formulated in terms of linear matrix inequalities. The proposed results are shown to be less conservative compared to other results from the literature. Some illustrative examples are given to show the effectiveness of the obtained results.     

区间变时滞不确定系统鲁棒稳定性分析

本文针对一类线性区间变时滞不确定系统的鲁棒稳定性分析问题进行了研究.基于时滞中点法和凸组合技术,借助于构造一个包含四重积分项的新Lyapunov-Krasovskii（L-K）泛函,并利用积分不等式方法给出了LMI（Linear Matrix Inequality）形式的时滞相关稳定性新判据.与已有文献相比,该判据能大大降低理论推导和计算上的复杂性.最后通过三个具有代表性的数值例子对比验证了本文所提出方法在降低结论保守性方面的优越性.     

New Synchronization Stability of Complex Networks With an Interval Time-Varying Coupling Delay

In this brief, the problem of synchronization stability analysis for complex dynamical networks with a time-varying coupling delay is studied. The delay considered in this brief is assumed to vary over an interval where the lower and upper bounds are known. By dividing the interval time-varying delay into a constant and a time-varying part and using a delay-partitioning approach, a new Lyapunov-Krasovskii functional is constructed. Based on this, a new delay-range-dependent criterion is obtained in terms of linear matrix inequalities. A numerical example is provided to show the effectiveness of the proposed results.     

A Linear Time-Varying Controller for Synchronization of LÜ Chaotic Systems With One Input

This brief addresses the problem of synchronization of two LÜ chaotic systems. As opposed to nonlinear Lyapunov-based controllers, which are designed with the aim of rendering the derivative of a Lyapunov function negative along trajectories of the closed-loop system, control design exploits the natural stability properties of the system. The proof relies not only on basic Lyapunov stability theory but also on other concepts, such as persistency of excitation. The contribution with respect to other works is to show that one control input is enough to force synchronization; moreover, the controllers are linear time varying.      

Synchronization of Coupled Neutral-Type Delay Partial Differential Systems

This paper considers the asymptotical synchronization and \(H_\infty \) synchronization for coupled neutral-type delay partial differential systems (NDPDSs). First, we construct a coupled synchronization error dynamic. Using the method of nonsingular matrix transformation, we decouple these coupled synchronization error dynamical systems. Then we study the asymptotical stability of the decoupled synchronization error dynamical systems through the Lyapunov–Krasovskii functional method, which implies the asymptotical synchronization of the coupled NDPDSs. Furthermore, when external disturbances enter the coupled NDPDSs, the \(H_\infty \) synchronization problem is also considered. The equivalence between the \(H_\infty \) stability of decoupled synchronization error dynamical systems and the \(H_\infty \) synchronization of coupled NDPDSs is proved by rigorous mathematical analysis. Then the criterion for the \(H_\infty \) stabilization is presented, which guarantees the \(H_\infty \) synchronization of the coupled NDPDSs. Moreover, as a remarkable difference between the ordinary differential systems and partial differential systems, the effect of the spatial domain on the synchronization is revealed through the obtained criteria. At last, numerical examples are given to illustrate the correctness of our results.     

Improved H ∞ Filtering for Systems with a Time-Varying Delay

This paper focuses on H _∞ filter design for systems with time-varying delay. A delay-dependent H _∞ performance analysis result is first established for error systems without ignoring any terms in the derivative of the Lyapunov functional by considering the relationship between the time-varying delay and its upper bound. Based on the derived H _∞ performance analysis result, the H _∞ filter is designed in terms of linear matrix inequalities (LMIs). The resulting criteria are extended to systems with polytopic-type uncertainties. Numerical examples are given to demonstrate the merits of the proposed method.     

A New Robust Stabilization Analysis Result for Uncertain Systems with Time-Varying Delay

Time delay and uncertainty are frequently encountered in various engineering systems. The robust stabilization problem for uncertain systems with time-delay has been paid more attentions by many researchers[1-8]. Most results of the robust stabilization are based on the systems matrices norm approach. The uncertainties of the systems discussed there must satisfy the so-called matching-conditions, which is more strict for the practical systems. The memoryless state feedback control gain matrice…     

Time and Frequency Synchronization with Channel Estimation for SC-FDMA Systems Over Time-Varying Channels

The constant amplitude zero autocorrelation sequence based synchronization and its usage in the block-type channel estimation for the single carrier frequency division multiple access (SC-FDMA) systems are vulnerable to the time-varying channels. Therefore, the channel estimation errors limit the performance of SC-FDMA systems in fast fading environments and result an irreducible error floor. In this paper, cyclic prefix based maximum likelihood estimator of time/frequency synchronization with comb-type channel estimation for the SC-FDMA systems are proposed to track the channel variations. Moreover, the residual time/frequency offsets calculations are derived for SC-FDMA systems. Simulation results confirm and illustrate that the proposed receiver is capable of tracking fast fading channel parameters and improving the overall performance as compared with the conventional receiver.     

Controller Failure Analysis for Systems with Interval Time-Varying Delay: A Switched Method

This paper studies the problem of controller failure analysis for a class of interval time-varying delay systems with a predesigned state feedback controller. Our objective is to establish conditions concerning controller failure time, under which the systems still keep exponentially stable. For this purpose, the systems with controller failures are first formulated as a class of switched delay systems. Next, based on a piecewise Lyapunov functional method, the exponential stability of such systems is guaranteed by restricting the unavailable rate and failure frequency of the controller. All the results are presented in terms of linear matrix inequalities. Two examples are provided to demonstrate the effectiveness of the proposed technique.     

On the Capacity of Time-Varying Channels With Periodic Feedback

The capacity of time-varying channels with periodic feedback at the transmitter is evaluated. It is assumed that the channel-state information (CSI) is perfectly known at the receiver and is fed back to the transmitter at the regular time intervals. The system capacity is investigated in two cases: 1) finite-state Markov channel, and 2) additive white Gaussian noise channel with time-correlated fading. In the first case, it is shown that the capacity is achievable by multiplexing multiple codebooks across the channel. In the second case, the channel capacity and the optimal adaptive coding is obtained. It is shown that the optimal adaptation can be achieved by a single Gaussian codebook, while adaptively allocating the total power based on the side information at the transmitter.     

Global Asymptotical Synchronization of Chaotic Lur'e Systems Using Sampled Data: A Linear Matrix Inequality Approach

Sampled-data feedback control for master-slave synchronization schemes that consist of identical chaotic Lur'e systems is studied. Sufficient conditions for global asymptotic synchronization of such chaotic Lur'e systems are obtained using the free-weighting matrix approach and expressed in terms of linear matrix inequalities (LMIs). With the help of the LMI solvers, the sampled-data feedback control law can easily be obtained to globally asymptotically synchronize Lur'e chaotic systems. The effectiveness of the proposed method is finally illustrated via numerical simulations of chaotic Chua's circuits.     

Stabilization of Switched Linear Systems with Time-Varying Delay in Switching Occurrence Detection

In this paper, we study stabilization of switched linear systems with time-varying delay in switching occurrence detection. The stabilization is realized through online and offline feedback mechanisms, respectively, and a state feedback controller design approach is proposed for each mechanism. To develop the main results, a more precise calculation method is proposed to estimate overshoots of transition matrices, which can be viewed as a refinement of existing results.     

Delay-Dependent Passivity and Passification for Uncertain Singularly Perturbed Markovian Jump Systems with Time-Varying Delay

This paper is concerned with passivity analysis and passivity-based controller design for uncertain singularly perturbed Markovian jump systems with time-varying delay in an interval. Firstly, a delay-dependent condition for the considered system to be mean-square exponentially stable and robustly passive is derived in terms of linear matrix inequality. Then, the passification problem is investigated. Based on the obtained passivity condition, the existence of the desired state feedback controller is established. Numerical examples are presented to show the effectiveness of the proposed method.