Delay-dependent sampled-data control based on delay estimates

In this paper the sampled-data stabilization of linear time-invariant systems with feedback delay is considered. We assume that the delay is time-varying and that its value is approximatively known. We investigate how to use the available information about the evolution of delays for adapting the control law in real time. Numerical methods for the design of a delay-dependent controller are presented. This allows for providing a control for some cases in which the stabilization cannot be ensured using a controller with a fixed structure.     

一般耦合结构时变时滞复杂网络的同步准则

研究一般耦合结构时变时滞复杂网络的同步问题,取消了复杂网络外部耦合矩阵是对称且不可简约的约束.对于一般的外部耦合矩阵,考虑了具有复数特征根的情况,并对复数域上的向量进行相应的处理.基于Lyapunov稳定性理论,利用矩阵分解技巧及线性矩阵不等式方法,通过构造适当的Lyapunov泛函,得到了网络系统实现同步的充分条件.为验证所得结论的有效性,对网络同步问题进行了数值仿真.仿真结果显示本文的同步准则较已有研究具有更小的保守性.     

时滞耦合和非时滞耦合的奇异复杂动态网络之同步性准则

本文利用李雅普诺夫稳定性理论,对时滞耦合和非时滞耦合的奇异复杂动态网络之同步获得了一些新的充分条件.这些条件均可转化为求解一组线性矩阵不等式(LMI).在降低准则保守性的过程中,本文充分运用了矩阵函数的凸性和自由权重矩阵理论.最后给出了两个数例;与已有文献做了比较,说明本文结论的有效性,以及较低的保守性.     

Stability analysis of bilinear systems under aperiodic sampled-data control

This note considers the problem of local stability of bilinear systems with aperiodic sampled-data linear state feedback control. The sampling intervals are time-varying and upper bounded. It is shown that the feasibility of some linear matrix inequalities (LMIs), implies the local asymptotic stability of the sampled-data system in an ellipsoidal region containing the equilibrium. The method is based on the analysis of contractive invariant sets, and it is inspired by the dissipativity theory. The results are illustrated by means of numerical examples.     

Exponential stability analysis for neutral BAM neural networks with time-varying delays and stochastic disturbances

This paper is concerned with the global exponential stability analysis problem for a class of neutral bidirectional associative memory (BAM) neural networks with time-varying delays and stochastic dist...     

Design of sampled-data control for multiple-time delayed generalised neural networks based on delay-partitioning approach

In this paper, we addressed the problem of stability analysis for a class of generalised mixed delayed neural networks by delay-partitioning approach. A novel integral inequality is developed by employing Wirtinger's integral inequality and Leibniz–Newton formula. By constructing an augmented Lyapunov–Krasovskii functional with triple and quadruple integral terms and using some standard integral inequality techniques, asymptotic stability criterion is obtained to the concerned neural networks. By converting the sampling period into a bounded time-varying delays, the error dynamics of the considered generalised neural networks are derived in terms of a dynamic system with sampling. Finally, numerical examples are given to show that the proposed method is less conservative than existing ones.     

Pinning adaptive synchronization of a general complex dynamical network

There are two challenging fundamental questions in pinning control of complex networks: (i) How many nodes should a network with fixed network structure and coupling strength be pinned to reach network synchronization? (ii) How much coupling strength should a network with fixed network structure and pinning nodes be applied to realize network synchronization? To fix these two questions, we propose a general complex dynamical network model and then further investigate its pinning adaptive synchronization. Based on this model, we attain several novel adaptive synchronization criteria which indeed give the positive answers to these two questions. That is, we provide a simply approximate formula for estimating the detailed number of pinning nodes and the magnitude of the coupling strength for a given general complex dynamical network. Here, the coupling-configuration matrix and the inner-coupling matrix are not necessarily symmetric. Moreover, our pinning adaptive controllers are rather simple compared with some traditional controllers. A Barabási-Albert network example is finally given to show the effectiveness of the proposed synchronization criteria.     

Improved results on synchronisation of delayed complex dynamical networks via sampled-data control

This paper focuses on the synchronisation problem of delayed complex dynamical networks via sampled-data control. A novel input-delay-dependent Lyapunov–Krasovskii functional (LKF) is constructed for the first time, which can make full use of the information on the input delay. To strengthen the combinations of the vectors in the resulting augmented vector, a new zero value equality is founded. Based on the input-delay-dependent LKF and zero value equality, synchronisation criteria are established. In comparison with some existing synchronisation criteria, the criteria in this paper are less conservative. The desired sampled-data controller is designed by solving a set of linear matrix inequalities. Finally, numerical examples are given to demonstrate the superiorities of proposed results.     

Synchronization of complex switched delay dynamical networks with simultaneously diagonalizable coupling matrices

This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when all subnetworks are synchronizable, a delay-dependent sufficient condition is given in terms of linear matrix inequalities （LMIs） which guarantees the solvability of the synchronization problem under an average dwell time scheme. We extend this result to the case that not all subnetworks are synchronizable. It is shown that in addition to average dwell time, if the ratio of the total activation time of synchronizable and non-synchronizable subnetworks satisfy an extra condition, then the problem is also solvable. Two numerical examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results.     

Improved results on synchronisation of Markovian jump complex dynamical networks via sampled-data controller and convex combination

This paper investigates the Markovian jump complex dynamical networks via a sampled-data controller and convex combination. Firstly, constructing an improved discontinuous Lyapunov-Krasovskii function (LKF), which is fully considered the characteristics of sampled-data to reduce the conservativeness. Secondly, designing an appropriate sample-data controller and combining some integral inequalities, convex function and free weighting matrices to utilise the upper bound on variable sampling interval and the sawtooth structure information of varying input delay. Then one can obtain the new criterion of sampled-data synchronisation. Finally, giving two examples to prove the effectiveness and superiority of the proposed methods. Obviously, compared with other existing literatures, this paper has less conservative.