A State-Observer-Based Approach for Synchronization in Complex Dynamical Networks

In this paper, a new approach for synchronization of complex dynamical networks is proposed based on state observer design. Unlike the common diagonally coupling networks, where full state coupling is typically needed between two nodes, here it is suggested that only a scalar coupling signal is required to achieve network synchronization. Some conditions for synchronization, in the form of an inequality, are established based on the Lyapunov stability theory, which can be transformed to a linear matrix inequality and easily solved by a numerical toolbox. Two typical dynamical network configurations, i.e., global coupling and nearest-neighbor coupling, with each node being a modified Chua's circuit, are simulated. It is demonstrated that the proposed scheme is effective in achieving the expected chaos synchronization in the complex network     

Fault Estimation for Nonlinear Dynamic Systems

In this paper, the problems of fault detection and estimation for nonlinear dynamic systems are considered by using fault detection observer and adaptive fault diagnosis observer. Based on Lyapunov stability theory and linear matrix inequality (LMI) techniques, a new sufficient condition in terms of LMIs for the proposed problem is derived. At the same time, we get the adaptive fault estimation algorithm. The LMI condition can be easily solved by MATLAB LMI toolbox. Finally, a flexible joint robotic example is given to illustrate the efficiency of the proposed approach.     

一类非线性互联系统的H∞模型参考跟踪分散输出反馈模糊控制

本文对一类不确定状态不可测非线性互联系统,给出了一种基于观测器的H_∞模型参考跟踪分散输出反馈模糊控制方法.设计中,首先采用模糊不确定T-S模型对非线性互联系统进行模糊建模,在此基础上,给出模糊分散观测器的H_∞设计和基于观测器的模型参考跟踪分散模糊控制的设计.应用李亚普诺夫和线性矩阵不等式方法给出了模糊分散系统稳定的充分条件.仿真结果进一步验证了所提出的模糊分散控制方法的有效性.     

Nonfragile Observer for Discrete-Time Switched Nonlinear Systems with Time Delay

This paper investigates the problem of the nonfragile observer design for discrete-time switched nonlinear systems with time delay. Based on the average dwell-time approach and linear matrix inequality (LMI) techniques, an exponential stability criterion for the discrete-time switched delay system with Lipschitz nonlinearity is derived. Based on several technical lemmas, the discrete-time observer design can be transferred to the problem of solving a set of LMIs. Furthermore, in cases when the gain of the state observer varies, a kind of nonfragile observer is proposed, and the solution to the observer gain is also obtained by solving a set of LMIs. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

Passivity-based fractional-order integral sliding-mode control design for uncertain fractional-order nonlinear systems

This paper concerns with the problem of designing a passivity-based fractional-order (FO) integral sliding mode controller for uncertain FO nonlinear systems. Utilizing the FO calculus, it is showed that the state trajectories of the closed-loop system reach the FO switching manifold in finite time. The control law ensures the asymptotical stability on the sliding surface. A parameter adjustment scheme for FO integral sliding surface is proposed by using the linear matrix inequality (LMI) approach. The proposed controller can be applied to different systems such as chaotic systems. Finally, simulation results are provided to show the effectiveness of the proposed method controlling chaos in FO Chua circuit and FO Van-der-Pol oscillator.     

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.     

Robust Non-Fragile Guaranteed Cost Control for Nonlinear Time Delay Discrete-Time Systems Based on T-S Model

This paper concerns the robust non-fragile guaranteed cost control for nonlinear time delay discrete-time systems based on Takagi-Sugeno （T-S） model. The problem is to design a guaranteed cost state feedback controller which can tolerate uncertainties from both models and gain variation. Sufficient conditions for the existence of such controller are given based on the linear matrix inequality （LMI） approach combined with Lyapunov method and inequality technique. A numerical example is given to illustrate the feasibility and effectiveness of our result.     

Observer-Based Optimal Fault Detection and Diagnosis Using Conditional Probability Distributions

A new optimal fault detection and diagnosis (FDD) scheme is studied in this paper for the continuous-time stochastic dynamic systems with time delays, where the available information for the FDD is the input and the measured output probability density functions (pdf's) of the system. The square-root B-spline functional approximation technique is used to formulate the output pdf's with the dynamic weightings. As a result, the concerned FDD problem can be transformed into a robust FDD problem subjected to a continuous time uncertain nonlinear system with time delays. Feasible criteria to detect and diagnose the system fault are provided by using linear matrix inequality (LMI) techniques. In order to improve FDD performances, two optimization measures, namely guaranteed cost performance and$H_infty$performance, are applied to optimize the observer design. Simulations are given to demonstrate the efficiency of the proposed approach.     

Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

This paper investigates the problem of stability analysis and stabilization for two-dimensional (2-D) discrete fuzzy systems. The 2-D fuzzy system model is established based on the Fornasini–Marchesini local state-space model, and a control design procedure is proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, nonquadratic stability conditions are derived by means of linear matrix inequality (LMI) technique. Then, by introducing an additional instrumental matrix variable, the stabilization problem for 2-D fuzzy systems is addressed, with LMI conditions obtained for the existence of stabilizing controllers. Finally, the effectiveness and advantages of the proposed design methods based on basis-dependent Lyapunov functions are shown via two examples.     

Delay-Probability-Distribution-Dependent Stability of Uncertain Stochastic Genetic Regulatory Networks with Time-Varying Delays

This paper investigates the delay-probability-distribution-dependent stability problem of uncertain stochastic genetic regulatory networks (SGRNs) with time-varying delays. The information of the probability distribution of the time-delay is considered and transformed into parameter matrices of the transferred SGRNs model. Based on the Lyapunov–Krasovskii functional and a stochastic analysis approach, a delay-probability-distribution-dependent sufficient condition is obtained in the linear matrix inequality (LMI) form such that delayed SGRNs are robustly globally asymptotically stable in the mean square for all admissible uncertainties. Three numerical examples are given to illustrate the effectiveness of our theoretical results.     

Delay-Dependent Exponential Stability Criterion for BAM Neural Networks with Time-Varying Delays

By employing the Lyapunov stability theory and linear matrix inequality（LMI）technique,delay-dependent stability criterion is derived to ensure the exponential stability of bi-directional associative memory（BAM）neural networks with time-varying delays.The proposed condition can be checked easily by LMI control toolbox in Matlab.A numerical example is given to demonstrate the effectiveness of our results.     

Anti-Synchronization of Markovian Jumping Stochastic Chaotic Neural Networks with Mixed Time Delays

The anti-synchronization control is investigated for a class of uncertain stochastic chaotic neural networks with both Markovian jump parameters and mixed delays. The mixed delays consists of discrete and distributed time-varying delays. First, by combining the Lyapunov method and a generalized Halanay-type inequality for stochastic differential equations, a delay-dependent criterion is established to guarantee the state variables of the discussed stochastic chaotic neural networks to be globally exponential anti-synchronized. Next, by utilizing a novel lemma and the Jensen integral inequality, a delay-dependent criterion is proposed to achieve the globally stochastic robust anti-synchronization. With some parameters being fixed in advance, the proposed conditions are all expressed in terms of linear matrix inequalities, which can be solved numerically by employing the standard Matlab LMI toolbox package. Finally, two examples are proposed to demonstrate the effectiveness and usefulness of the proposed results.     

A Nonlinear Adaptive Resilient Observer Design for a Class of Lipschitz Systems Using LMI

This paper addresses the parameter and state estimation problem in the presence of the observer gain perturbations for Lipschitz systems that are linear in the unknown parameters and nonlinear in the states. A nonlinear adaptive resilient observer is designed, and its stability conditions based on the Lyapunov technique are derived. The gain for this observer is derived systematically using the linear matrix inequality approach. A numerical example and a physical setup are provided to show the effectiveness of the proposed method.     

Parameter-Dependent Lyapunov Function Method for a Class of Uncertain Nonlinear Systems with Multiple Equilibria

First, a new linear matrix inequality (LMI) characterization of extended strict positive realness is presented for linear continuous-time systems. Then a class of nonlinear systems with multiple equilibria subject to polytopic uncertainty is addressed by the parameter-dependent Lyapunov function method. New sufficient conditions for global convergence are presented. This allows the Lyapunov function to be parameter dependent. Furthermore, an LMI-based controller design method is also given, and reduced-order controllers can be designed by performing a structural constraint on the introduced slack variables. Several numerical examples are included to demonstrate the applicability of the proposed method.     

Stabilization of Uncertain Singularly Perturbed Systems With Pole-Placement Constraints

This brief considers the problem of stabilization of uncertain singularly perturbed systems with pole-placement constraints by using$H^infty$dynamic output feedback design. Based on the Lyapunov stability theorem and the tool of linear matrix inequality (LMI), we solve dynamic output feedback gain matrices and a set of common positive-definite matrices, and then some sufficient conditions are derived to stabilize the singularly perturbed systems with parametric uncertainties. Moreover, the developed$H^infty$criterion guarantees that the influence of external disturbance is as small as possible and the poles of the closed-loop system are all located inside the LMI stability region. By the guaranteed$varepsilon$-bound issue, the proposed scheme can stabilize the systems for all$varepsilonin(0,varepsilon^ast)$. A circuit system is given to illustrate the validity of the proposed schemes.     

多时滞Cohen-Grossberg神经网络鲁棒稳定性的新判据

分析了一类具有多时滞及参数摄动的Cohen-Grossberg神经网络的全局鲁棒稳定性.通过构造适当的Lyapunov泛函,以线性矩阵不等式形式给出了平衡点全局鲁棒稳定的判据.此外,所有结论的建立都不需要假定互连矩阵的对称性及激活函数的可微性和单调性.仿真结果进一步证明了结论的有效性.     

Robust Stabilization of Delayed Singular Systems with Linear Fractional Parametric Uncertainties

This paper deals with the problem of robust stabilization for delayed singular systems with parametric uncertainties. The parametric uncertainties are assumed to be of a linear fractional form involving all system matrices. Necessary and sufficient conditions for quadratic stability and quadratic stabilization are obtained. Moreover, the results generalize and improve previous works on delayed singular systems with norm-bounded parametric uncertainties. A strict linear matrix inequality (LMI) design approach is developed such that, when the LMI is satisfied, a desired robust state feedback control law can be constructed. A numerical example is provided to demonstrate the application of the proposed method.     

多比例时滞细胞神经网络的同步性

基于混沌同步控制在保密通信及优化等诸多范畴的遍及应用,本文研究一类驱动-响应系统的同步性问题,包含指数同步性和多项式同步性.这里以一类带多比例时滞的细胞神经网络作为驱动系统,一类不带比例时滞的细胞神经网络作为响应系统.在激活函数满足Lipschitz的条件下,通过设计合适的时滞依赖的控制器,且利用Lyapunov稳定性理论及一些不等式分析探讨误差系统的稳定性,进而得到所研究的驱动-响应系统同步性的两个判定标准,然后给出数值模拟验证所得结果.