State estimation of recurrent neural networks with time-varying delay: A novel delay partition approach

The state estimation problem is studied in this paper for a class of recurrent neural networks with time-varying delay. A novel delay partition approach is developed to derive a delay-dependent condition guaranteeing the existence of a desired state estimator for the delayed neural networks. The design of the gain matrix of the state estimator can be achieved by solving a linear matrix inequality, where no slack variable is involved. A numerical example is finally provided to show the advantage of the proposed approach over some existing results.     

Delay-dependent state estimation for delayed neural networks

In this letter, the delay-dependent state estimation problem for neural networks with time-varying delay is investigated. A delay-dependent criterion is established to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable. The proposed method is based on the free-weighting matrix approach and is applicable to the case that the derivative of a time-varying delay takes any value. An algorithm is presented to compute the state estimator. Finally, a numerical example is given to demonstrate the effectiveness of this approach and the improvement over existing ones.     

Delay-dependent exponential state estimators for stochastic neural networks of neutral type with both discrete and distributed delays

This paper considered the state estimation for stochastic neural networks of neutral type with discrete and distributed delays. By using available output measurements, the state estimator can approximate the neuron states, and the asymptotic property of the state error is mean square exponential stable and also almost surely exponential stable in the presence of discrete and distributed delays. Under the Lipschitz assumptions for the activation functions and the measurement nonlinearity, a delay-dependent linear matrix inequality (LMI) criterion is proposed to guarantee the existence of the desired estimators by constructing an appropriate Lyapunov-Krasovskii function. It is shown that the existence conditions and the explicit expression of the state estimator can be parameterised in terms of the solution to a LMI. Finally, two numerical examples are presented to demonstrate the validity of the theoretical results and show that the theorem can provide less conservative conditions.     

Robust State Estimation for Delayed Complex-Valued Neural Networks

This paper is concerned with the state estimation problem for the uncertain complex-valued neural networks with time delays. The parameter uncertainties are assumed to be norm-bounded. Through available output measurements containing nonlinear Lipschitz-like terms, we aim to design a state estimator to estimate the complex-valued network such that, for all admissible parameter uncertainties and time delay, the dynamics of the error-state system is guaranteed to be globally asymptotically stable. In addition, the case that there are no parameter uncertainties is also considered. By utilizing the Lyapunov functional method and matrix inequality techniques, some sufficient delay-dependent criteria are derived to assure the existence of the desired estimator gains. Finally, two numerical examples with simulations are presented to demonstrate the effectiveness of the proposed estimation schemes.     

State Estimation for Coupled Uncertain Stochastic Networks With Missing Measurements and Time-Varying Delays: The Discrete-Time Case

This paper is concerned with the problem of state estimation for a class of discrete-time coupled uncertain stochastic complex networks with missing measurements and time-varying delay. The parameter uncertainties are assumed to be norm-bounded and enter into both the network state and the network output. The stochastic Brownian motions affect not only the coupling term of the network but also the overall network dynamics. The nonlinear terms that satisfy the usual Lipschitz conditions exist in both the state and measurement equations. Through available output measurements described by a binary switching sequence that obeys a conditional probability distribution, we aim to design a state estimator to estimate the network states such that, for all admissible parameter uncertainties and time-varying delays, the dynamics of the estimation error is guaranteed to be globally exponentially stable in the mean square. By employing the Lyapunov functional method combined with the stochastic analysis approach, several delay-dependent criteria are established that ensure the existence of the desired estimator gains, and then the explicit expression of such estimator gains is characterized in terms of the solution to certain linear matrix inequalities (LMIs). Two numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes.     

New exponentially convergent state estimation method for delayed neural networks

The problem of designing a globally exponentially convergent state estimator for a class of delayed neural networks is investigated in this paper. The time-delay pattern is quite general and including fast time-varying delays. The activation functions are monotone nondecreasing with known lower and upper bounds. A linear estimator of Luenberger-type is developed and by properly constructing a new Lyapunov–Krasovskii functional coupled with the integral inequality, the global exponential stability conditions of the error system are derived. The unknown gain matrix is determined by solving a delay-dependent linear matrix inequality. The developed results are shown to be less conservative than previously published ones in the literature, which is illustrated by a representative numerical example.     

Reliable finite-time H∞ control of uncertain singular nonlinear Markovian jump systems with bounded transition probabilities and time-varying delay

This paper investigates the problem of reliable finite-time H_∞ control for one class of uncertainsingular nonlinear Markovian jump systems with time-varying delay subject to partial information on the transition probabilities. Continuous fault model is more general and practical to serve as the actuator fault. Time delay is a kind of positive time-varying differentiable bounded delays. First, based on a state estimator the resulting closed-loop error system is constructed and sufficient criteria are provided to guarantee that the augmented system is singular stochastic finite-time boundedness and singular stochastic H_∞ finite-time boundedness in both normal and fault cases via constructing a delay-dependent Lyapunov–Krasonskii function. Then, the gain matrices of state-feedback controller and state estimator are fixed by solving a feasibility problem in terms of linear matrix inequalities through decoupling technique, respectively. Finally, numerical examples are given to show the validity of the proposed design approach.     

Guaranteed performance state estimation of static neural networks with time-varying delay

This paper is concerned with studying two kinds of guaranteed performance state estimation problems for static neural networks with time-varying delay. Both delay-independent and delay-dependent design criteria are presented under which the resulting estimation error system is globally asymptotically stable and a prescribed performance is guaranteed in the H_∞ or generalized H₂ sense. It is shown that the gain matrices of the state estimator and the optimal performance indexes can be simultaneously obtained by solving convex optimization problems subject to linear matrix inequalities. It is worth noting that no slack variable is introduced in the proposed conditions, and thus the computational burden is reduced. The effectiveness of the developed results is finally demonstrated by simulation examples.     

不确定时滞系统鲁棒镇定新方法

针对一类同时具有状态和控制滞后的不确定时滞系统,提出了一种新的时滞依赖型鲁棒镇定设计方法.通过引入一种新的线性状态变换,分离出时滞依赖因子,采用Lyapunov-Krasovskii泛函方法,导出了不确定时滞系统可鲁棒镇定的时滞依赖型的新判据,所得结论以线性矩阵不等式组的解的形式表示.仿真结果表明所得结论较之已有结果更为简单,具有更小保守性,且有更广泛的应用范围,不仅可以解决小时滞问题,也可用于解决大时滞问题.     

广义时滞系统时滞依赖H∞控制的改进结果

讨论广义时滞系统的时滞依赖控制问题. 基于线性矩阵不等式(LMI)方法和增广Lyapunov泛函, 给出保证系统正则、无脉冲、稳定且满足性能指标的时滞依赖有界实引理. 在此引理的基础上, 给出基于严格LMI的状态反馈控制器存在的时滞依赖条件. 同时给出所需状态反馈控制器的明确表示. 数值例子表明本文的结果改进了已有结论的保守性.     

Delay-dependent robust asymptotic state estimation of Takagi-Sugeno fuzzy Hopfield neural networks with mixed interval time-varying delays

This paper investigates delay-dependent robust asymptotic state estimation of fuzzy neural networks with mixed interval time-varying delay. In this paper, the Takagi-Sugeno (T-S) fuzzy model representation is extended to the robust state estimation of Hopfield neural networks with mixed interval time-varying delays. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time delays, the dynamics of the estimation error is globally asymptotically stable. Based on the Lyapunov-Krasovskii functional which contains a triple-integral term, delay-dependent robust state estimation for such T-S fuzzy Hopfield neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. The unknown gain matrix is determined by solving a delay-dependent LMI. Finally two numerical examples are provided to demonstrate the effectiveness of the proposed method.     

$$H_\infty $$ state estimation of stochastic neural networks with mixed time-varying delays

This paper is concerned with \(H_\infty \) state estimation problem of stochastic neural networks with discrete interval and distributed time-varying delays. The time-varying delay is need to be bounded and continuous. By constructing a suitable Lyapunov–Krasovskii functional with triple integral terms and linear matrix inequality technique, the delay-dependent criteria are conferred so that the error system is stochastically asymptotically mean-square stable with \(H_\infty \) performance. The desired estimator gain matrix can be characterized in terms of the solution to linear matrix inequalities, which can be easily solved by some standard numerical algorithms. Numerical simulations are given to demonstrate the effectiveness of the proposed method. The results are also compared with existing methods.     

Robust stability analysis of singular linear system with delay and parameter uncertainty

1Introduction It is well known that the existence of a delay in adynamical system may induce instability or poorperformances in various systems suchas electric,pneumatic,and hydraulic networks,chemical processes,longtransmission lines,etc.For a survey of time_delay systems,the reader can refer to a recent overview paper[1].Control of singular systems has been extensively studied inthe past years due to the fact that singular systems betterdescribe physical systems than regular ones.Agreat numb…     

一类时滞不确定随机系统的鲁棒控制的新方法

针对一类不确定含输入控制时滞的随机系统,提出了一种新的时滞相关鲁棒控制设计方法,利用线性状态变换、构造Lyapunov-Krasovskii泛函,在线性反馈控制律的作用下,获得了闭环系统依赖于时滞的稳定性条件.所得结论以线性矩阵不等式的形式表示.最后通过数值例子说明该方法的有效性.     

Fault estimator design for a class of switched systems with time-varying delay

This article studies the problem of fault estimator design for switched time-delay systems with impulsive control. The delay signal is assumed to be uniformly bounded, differentiable and has a bounded derivative. The problem is first formulated in the framework of H _∞ filtering by incorporating a priori knowledge of the fault into the design procedure. A hybrid controller, composed of a fault estimator and an impulsive controller, is constructed. Some delay-dependent sufficient conditions are derived on the existence of the hybrid controller by using the multiple Lyapunov functional approach. In addition, based on the cone complementarity algorithm, the solutions to the parameter matrices are obtained by solving a set of linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.     

Robust control for a class of T-S fuzzy systems with interval time-varying delay

The problem of delay-dependent stability analysis and controller design for a class of T-S fuzzy systems with interval state time-varying delay is considered. Based on Lyapunov stability theory, defining a new Lyapunov-Krasovskii functional and introducing some free-weighting matrices, a new delay-dependent criterion is given to ensure the systems asymptotically stable. The merit of the proposed conditions lies in the less conservativeness than the existing ones, which is achieved by considering the mean of time-delay interval and the introduction of the free variables. By the concept of parallel distributed compensation (PDC), a delay-dependent condition for the existence of a fuzzy state feedback control law with memory is proposed. Another merit is the consideration of the memory of the controller. All conditions are shown in terms of linear matrix inequalities (LMIs), which can be solved efficiently by using the LMI optimization techniques. Two numerical examples are given to illustrate the feasibility and validity of the proposed approach.     

线性时滞系统依赖于时滞的H∞状态反馈控制

对具有纯滞后输入的线性时滞系统,在系统的状态时滞与控制输入时滞不同时,研 究了依赖时滞的H∞状态反馈控制器设计问题,其控制器存在的充分条件由一个线性矩阵不 等式(LMI)的形式给出,并给出了相应的H∞控制器的综合设计方法.     

一类线性时滞系统的鲁棒稳定性分析

针对一类具有范数有界不确定性和2个继发时变时滞的线性时滞不确定系统,研究了其时滞依赖鲁棒稳定性问题.通过定义充分利用时变时滞上下界信息的新型Lyapunov-Krasovskii泛函,并结合时滞系统相关处理方法和线性矩阵不等式方法,得到了时滞线性不确定系统鲁棒渐近稳定所满足的条件.为了降低结论的保守性,对某些项进行了较紧致的估计.此外,并未引入自由权矩阵.最后并通过2个数值仿真证实了方法的有效性和优越性.     

Delay-dependent stability analysis and stabilization for discrete-time fuzzy systems with state delay: a fuzzy Lyapunov-Krasovskii functional approach.

This correspondence studies stability analysis and stabilization for discrete-time Takagi and Sugeno fuzzy systems with state delay. First, a new fuzzy Lyapunov-Krasovskii functional (LKF) is constructed to derive a delay-dependent stability condition for open-loop fuzzy systems. Then, a delay-dependent stabilization approach based on a nonparallel distributed compensation scheme is provided for closed-loop fuzzy systems. Both state feedback and observer-based control cases are considered. The proposed stability and stabilization conditions are represented in terms of linear matrix inequalities (LMIs), which can be solved efficiently by using existing LMI optimization techniques. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.     

Robust stability analysis of singular linear system with delay and parameter uncertainty

This paper deals with th e problem of robust stability for continuous-time sin gular systems with state delay and parameter uncerta inty.The uncertain singular systems with delay consi dered in this paper are assumed to be regular and impulse free.By decomposing the systems into slow and fast subsystems,a robust delay-dependent asymptotic stability criteria based on linear matrix inequality is proposed,which is derived by using Lyapunov-Krasovskii functionals,neither model transformatio n nor bounding for cross terms is required in the derivation of our delay-dependent result.The r obust delay-dependent stability criterion proposed in th is paper is a sufficient condition.Finally,numerical examples and Matlab simulation are provided to illustrate the effectiveness of the proposed method.