Advanced sampled-data synchronization control for complex dynamical networks with coupling time-varying delays

New results on stability and H∞ performance analysis for aperiodic sampled-data systems via augmented Lyapunov functional

This paper focuses on the stability and H_∞ performance analysis problems for aperiodic sampled-data systems. An augmented Lyapunov functional is commonly used to study the stability issue based on Lyapunov-Krasovskii theory. To obtain less-conservative results for aperiodic sampled-data systems, an improved augmented Lyapunov functional, which includes the sampling-instant-dependent state variables more fully, is presented on the basis of the double-side looped-functional technique. This functional provides sufficient cross-terms among state variables, which helps to reduce the conservatism. By the functional, the asymptotical stability and H_∞ performance analysis of the aperiodic sampled-data systems are studied. In the end, four numerical examples are given to verify the superiority of the proposed methods.

Finite-Time Synchronization for Delayed Complex Dynamical Networks With Synchronizing or Desynchronizing Impulses

In this article, the finite-time synchronization problem of delayed complex dynamical networks (CDNs) with impulses is studied, where two types of impulses, namely, synchronizing impulses and desynchronizing impulses, are fully considered, respectively. Since the existence of impulses makes the discontinuity of the states, which means that the classical result for finite-time stability is inapplicable in such a case, the key challenge is how to guarantee the finite-time stability and estimate the settling time in impulse sense. We apply impulsive control theory and finite-time stability theory to CDNs and establish some sufficient conditions for finite-time synchronization, where two kinds of memory controllers are designed for synchronizing impulses and desynchronizing impulses, respectively. Moreover, the upper bounds for settling time of synchronization, which depends on the impulse sequences, are effectively estimated. It shows that the synchronizing impulses can shorten the settling time of synchronization; conversely, the desynchronizing impulses can delay it. Finally, the theoretical analysis is verified by two simulation examples.

Exponential Synchronization and L2 -Gain Analysis of Delayed Chaotic Neural Networks Via Intermittent Control With Actuator Saturation

By using an intermittent control approach, this paper is concerned with the exponential synchronization and L₂ -gain analysis for a class of delayed master-slave chaotic neural networks subject to actuator saturation. Based on a switching strategy, the synchronization error system is modeled as a switched synchronization error system consisting of two subsystems, and each subsystem of the switched system satisfies a dwell time constraint due to the characteristics of intermittent control. A piecewise Lyapunov-Krasovskii functional depending on the control rate and control period is then introduced, under which sufficient conditions for the exponential stability of the constructed switched synchronization error system are developed. In addition, the influence of the exogenous perturbations on synchronization performance is constrained at a prescribed level. In the meantime, the intermittent linear state feedback controller can be derived by solving a set of linear matrix inequalities. More incisively, the proposed method is also proved to be valid in the case of aperiodically intermittent control. Finally, two simulation examples are employed to demonstrate the effectiveness and potential of the obtained results.

Synchronization of complex dynamical networks with random coupling delay and actuator faults

This paper addresses the issue of passivity-based synchronization problem for a family of Markovian jump neutral complex dynamical networks (NCDNs) with coupling delay and actuator faults. Also, by considering the effect of random fluctuation in complex dynamical network systems, the occurrence of coupling delay are taken in terms of a stochastic distribution, which obeys the Bernoulli distribution. To handle the fault effects in actuators of proposed complex network systems, an actuator fault model is considered. The main objective of this paper is to develop a robust state feedback controller such that for all possible actuator failures and random coupling delays, all nodes of the proposed Markovian jump NCDNs is globally asymptotically synchronized to the reference node in mean square sense and guarantee the output strict passivity performance. By developing a suitable Lyapunov-Krasovskii functional and utilizing the Wirtinger-based integral inequality, the required a set of sufficient conditions for the synchronization of proposed system is established in form of linear matrix inequalities. Finally, three numerical examples including a 3-dimensional Lorenz chaotic model are provided to demonstrate the correctness and superiority of the proposed control scheme.

Disturbance and uncertainty rejection performance for fractional-order complex dynamical networks

This paper investigates the synchronization issue for a family of time-delayed fractional-order complex dynamical networks (FCDNs) with time delay, unknown bounded uncertainty and disturbance. A novel fractional uncertainty and disturbance estimator (FUDE) based feedback control strategy is proposed to not only synchronize the considered FCDNs but also guaranteeing the precise rejection of unmodelled system uncertainty and external disturbance. Especially, in FUDE-based approach, model uncertainties and external disturbance are integrated as a lumped disturbance and it does not require a completely known system model or a disturbance model. On the other hand, the design algorithm for the proposed control strategy is based on the state-space framework, rather than frequency-based design methodologies in the literature, which helps for predominant comprehension of the inner system behaviour. Also, by the temperance of Lyapunov stability theory and fractional calculus, a set of adequate conditions in the linear matrix inequality framework is obtained, which guarantees the robust synchronization of the closed-loop system. Furthermore, an iterative optimization algorithm is proposed to improve control robustness against the external disturbance and model uncertainties. Finally, two numerical illustrations including financial network model, where the influence of adjustment of macro-economic policies in the entire financial system are given to exhibit the rightness and important features of the acquired theoretical results.