Delay-Dependent Robust Exponential Stability of Impulsive Markovian Jumping Reaction-Diffusion Cohen-Grossberg Neural Networks

This paper is devoted to investigating delay-dependent robust exponential stability for a class of Markovian jump impulsive stochastic reaction-diffusion Cohen-Grossberg neural networks (IRDCGNNs) with mixed time delays and uncertainties. The jumping parameters, determined by a continuous-time, discrete-state Markov chain, are assumed to be norm bounded. The delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. By constructing a Lyapunov–Krasovskii functional, and using poincarè inequality and the mathematical induction method, several novel sufficient criteria ensuring the delay-dependent exponential stability of IRDCGNNs with Markovian jumping parameters are established. Our results include reaction-diffusion effects. Finally, a Numerical example is provided to show the efficiency of the proposed results.     

具有区间时变时滞2-D 离散系统的时滞相关稳定与控制

针对具有区间时变时滞2-D离散系统,利用时滞相关方法,研究其稳定性与控制问题.首先选取含有时滞项上、下界的一个新的Lyapunov函数,对其差分时考虑所有项,得到了基于线性矩阵不等式(LMI)的时滞相关稳定性准则;然后给定时变时滞项的下界,再由一个凸优化问题最大化其上界,进而通过状态反馈实现系统的时滞相关控制,且求解LMI可得到增益矩阵;最后,利用数值算例说明了所得结果有效且优于已有成果.     

具有时变状态滞后2-D离散系统的稳定与镇定(英文)

针对一类由局部状态空间(LSS)Fornasini-Marchesini(FM)第二模型描述的,具有时变状态滞后的2-D离散系统,其中时变滞后项的上、下界均为正实数,研究了其稳定性和控制综合问题。首先,利用Lyapunov-Krasovski泛函方法,提出了系统的稳定性准则。再根据这一准则,分别设计状态反馈和动态输出反馈控制器保证系统的稳定性。状态反馈控制律和输出反馈矩阵可由线性矩阵不等式(LMI)求得。最后,通过数值算例说明所得结果的有效性。     

Delay dependent stability results for fuzzy BAM neural networks with Markovian jumping parameters

This paper deals with the delay-dependent asymptotic stability analysis problem for a class of fuzzy bidirectional associative memory (BAM) neural networks with time-varying interval delays and Markovian jumping parameters by Takagi–Sugeno (T–S) fuzzy model. The nonlinear delayed BAM neural networks are first established as a modified T–S fuzzy model in which the consequent parts are composed of a set of Markovian jumping BAM neural networks with time-varying interval delays. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite-state space. The new type of Markovian jumping matrices P_k and Q_k are introduced in this paper. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. A new delay-dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov–Krasovskii functional and introducing some free-weighting matrices. Numerical examples are given to demonstrate the effectiveness of the proposed methods.     

Delay-interval-dependent robust-stability criteria for neutral stochastic neural networks with polytopic and linear fractional uncertainties

In this paper, the delay-interval-dependent robust stability is studied for a class of neutral stochastic neural networks with time-varying delays. The time-varying delay is assumed to belong to an interval, which means that the upper bound is known and the lower bound is not restricted to zero. For the neural networks under study, the uncertainty includes polytopic uncertainty and linear fractional norm-bounded uncertainty. Sufficient conditions for the stability of the addressed neutral stochastic neural networks with time-varying delays are established by employing the proper Lyapunov–Krasovskii functional, a combination of the stochastic analysis theory, some inequality techniques and new linear matrix inequality (LMI). Finally, three numerical examples are provided to demonstrate less conservatism and effectiveness of the proposed LMI conditions.     

On designing memory state feedback controller for linear systems with interval time-varying delay

This paper is concerned with the design of a memory state feedback controller for linear systems with interval time-varying delays. The time delay is assumed to be a time-varying continuous function belonging to a given interval, which means that the lower and upper bounds of time-varying delay are available. First, a less conservative delayrange-dependent stability criteria is proposed by using a new interval fraction method. In the process of controller synthesis, the history information of system is considered in the controller design by introducing the lower delay state. Moreover, the usual memoryless state feedback controller for the underlying systems could be considered as a special case of the memory case. Finally, two numerical examples are given to show the effectiveness of the proposed method.     

Robust Stability for Uncertain Delayed Fuzzy Hopfield Neural Networks With Markovian Jumping Parameters

This paper is concerned with the problem of the robust stability of nonlinear delayed Hopfield neural networks (HNNs) with Markovian jumping parameters by Takagi-Sugeno (T-S) fuzzy model. The nonlinear delayed HNNs are first established as a modified T-S fuzzy model in which the consequent parts are composed of a set of Markovian jumping HNNs with interval delays. Time delays here are assumed to be time-varying and belong to the given intervals. Based on Lyapunov-Krasovskii stability theory and linear matrix inequality approach, stability conditions are proposed in terms of the upper and lower bounds of the delays. Finally, numerical examples are used to illustrate the effectiveness of the proposed method.     

具有时变状态滞后的非线性2-D 离散系统的稳定性与控制

考虑一类由局部状态空间Fornasini-Marchesini(FM LSS)第二模型描述的,具有时变状态滞后非线性二维(2-D)离散系统的稳定性分析和控制问题.时变状态滞后项的上、下界为正整数,非线性项满足Lipschitz条件.首先,通过引入一个含有时滞上、下界的新Lyapunov函数,给出了系统的稳定性准则;然后设计了状态反馈控制器以保证系统的稳定性,进而,状态反馈控制律可由线性矩阵不等式求得;最后通过数值算例表明了所得结果的有效性.     

基于Jensen 不等式的2-D 区间时变时滞系统的稳定与控制

考虑具有区间时变时滞二维(2-D) 离散系统的时滞相关稳定性和控制问题. 选取含有时滞上下界的Lyapunov 函数, 对其差分时考虑到所有项, 结合2-DJensen 不等式, 由线性矩阵不等式给出系统新的时滞相关稳定性准则. 准则中含有更少的待定变量, 降低了数值计算负担, 并且比一些已有结果具有更小的保守性. 基于稳定性准则, 由状态反馈实现了系统的稳定控制. 最后, 通过数值算例表明了所得结果的有效性和优越性.

     

Design of delay-range-dependent robust controller for uncertain genetic regulatory networks with interval time-varying delays

This paper investigates the problem of robust stabilization for genetic regulatory networks with interval time-varying delays, which are subject to norm-bounded time-varying parameter uncertainties. The time delays including lower and upper bounds of delay are assumed to appear in both the mRNA and protein. The regulatory functions are assumed to be globally Lipschitz continuous. The resulting delay-range-dependent robust controller with interval range is designed in terms of improved bounding technique. A sufficient condition for the solvability of the problem is obtained via a linear matrix inequality (LMI). When this LMI is feasible, an explicit expression of a desired state feedback controller is also given. The theory developed in this paper is demonstrated by two numerical examples.     

Event-triggered state estimation for Markovian jumping impulsive neural networks with interval time-varying delays

This paper investigates the event-triggered state estimation problem of Markovian jumping impulsive neural networks with interval time-varying delays. The purpose is to design a state estimator to estimate system states through available output measurements. In the neural networks, there are a set of modes, which are determined by Markov chain. A Markovian jumping time-delay impulsive neural networks model is employed to describe the event-triggered scheme and the network- related behaviour, such as transmission delay, data package dropout and disorder. The proposed event-triggered scheme is used to determine whether the sampled state information should be transmitted. The discrete delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. First, we design a state observer to estimate the neuron states. Second, based on a novel Lyapunov-Krasovskii functional (LKF) with triple-integral terms and using an improved inequality, several sufficient conditions are derived. The derived conditions are formulated in terms of a set of linear matrix inequalities , under which the estimation error system is globally asymptotically stable in the mean square sense. Finally, numerical examples are given to show the effectiveness and superiority of the results.     

Stochastic Stability for a Class of Discrete-time Switched Neural Networks with Stochastic Noise and Time-varying Mixed Delays

In this paper, stochastic stability is analyzed for a class of discrete-time switched neural networks, in which time-varying mixed delays and stochastic noise are considered. Specifically, benefitting from the triple summation term included in a new Lyapunov functional, time-varying distributed delays are tackled and a criterion of decay estimation for a non-switched neural network is firstly obtained. Subsequently, in view of average dwell time methodology and stochastic analysis, several sufficient conditions are obtained to ensure that the stochastic stability problem is solvable. Furthermore, the derived sufficient conditions reflect that the decay rate of the considered neural networks has a close relationship with average dwell time, upper and lower bounds of delays and intensity of stochastic noise. Finally, validity of the inferred conclusions is given by a simulated example.     

Mean-square exponential stability of impulsive stochastic time-delay systems with delayed impulse effects

This paper is concerned with the mean-square exponential stability problem for a class of impulsive stochastic systems with delayed impulses. The delays exhibit in both continuous subsystem and discrete subsystem. By constructing piecewise time-varying Lyapunov functions and Razumikhin technique, sufficient conditions are derived which guarantee the mean-square exponential stability for impulsive stochastic delay system. It is shown that the obtained stability conditions depend both on the lower bound and the upper bound of impulsive intervals, and the stability of system is robust with regard to sufficiently small impulse input delays. Finally, two examples are proposed to verify the efficiency of the proposed results.     

Stabilisation for Markovian jump delta operator systems with time-varying delays and actuator saturation

In this paper, stochastic stabilisation is studied for Markovian jump delta operator systems with time-varying delays and actuator saturation. The transition probability rates in Markovian jump parameters are considered as partly known. Both lower and upper bounds are considered in the time-varying delays. Using Lyapunov–Krasovkii functional, a stochastic stabilisation condition is obtained for the closed-loop Markovian jump delta operator system with time-varying delays and actuator saturation. A numerical example is shown to illustrate the effectiveness and potential for the developed techniques.     

Robust stability for uncertain genetic regulatory networks with interval time-varying delays

This paper addresses the problem of robust stability of uncertain genetic regulatory networks (GRNs) with interval time-varying delays. We derive some new delay-range-dependent and delay-derivative-dependent/independent stability criteria by employing some free-weighting matrices and linear matrix inequalities. In our analysis, we carefully consider the relationship between the time-varying state delays and their bounds when calculating the upper bound of the derivative of Lyapunov functional. We hence show that, the rigorous requirement of other literatures that the time-derivatives of time-varying delays must be smaller than one is abandoned in the proposed scheme. The new criteria are applicable to both fast and slow time-varying delays. Finally, four numerical examples are presented to illustrate the effectiveness and the less conservativeness of the developed results.     

Decentralized H∞ control for large-scale interconnected nonlinear time-delay systems via LMI approach

In this paper, the problem of H_∞ control of nonlinear large-scale systems with interval time-varying delays in interconnection is considered. The time delays are assumed to be any continuous functions belonging to a given interval involved in both the state and observation output. By constructing a set of new Lyapunov–Krasovskii functionals, which are mainly based on the information of the lower and upper delay bounds, a new delay-dependent sufficient condition for the existence of decentralized H_∞ control is established in terms of linear matrix inequalities (LMIs). The approach is applied to decentralized H_∞ control of uncertain linear systems with interval time-varying delay. Numerical examples are given to show the effectiveness of the obtained results.     

H ∞ filtering for nonlinear singular Markovian jumping systems with interval time-varying delays

The problem of H _∞ filtering for nonlinear singular Markovian jumping systems with interval time-varying delays is investigated. The delay factor is assumed to be time-varying and belongs to a given interval, which means that the lower and upper bounds of the interval time-varying delays are available. Furthermore, the derivative of the time-varying delay function can be larger than one. With partial knowledge of the jump rates of the Markov process, a new delay-range-dependent bounded real lemma for the solvability of the jump system is obtained based on the Lyapunov–Krasovskii functional, which is in terms of strict linear matrix inequalities (LMIs). When these LMIs are feasible, an expression of a desired H _∞ filter is given. Numerical examples are given to illustrate the effectiveness of the developed techniques.     

Delay‐dependent Stability and Static Output Feedback Control of 2‐D Discrete Systems with Interval Time‐varying Delays

This paper is concerned with the problems of delay‐dependent stability and static output feedback (SOF) control of two‐dimensional (2‐D) discrete systems with interval time‐varying delays, which are described by the Fornasini‐Marchesini (FM) second model. The upper and lower bounds of delays are considered. Applying a new method of estimating the upper bound on the difference of Lyapunov function that does not ignore any terms, a new delay‐dependent stability criteria based on linear matrix inequalities (LMIs) is derived. Then, given the lower bounds of time‐varying delays, the maximum upper bounds in the above LMIs are obtained through computing a convex optimization problem. Based on the stability criteria, the SOF control problem is formulated in terms of a bilinear matrix inequality (BMI). With the use of the slack variable technique, a sufficient LMI condition is proposed for the BMI. Moreover, the SOF gain can be solved by LMIs. Numerical examples show the effectiveness and advantages of our results.     

New conditions for delay-derivative-dependent stability

Two recent Lyapunov-based methods have significantly improved the stability analysis of time-delay systems: the delay-fractioning approach of Gouaisbaut and Peaucelle (2006) for systems with constant delays and the convex analysis of systems with time-varying delays of Park and Ko (2007). In this paper we develop a convex optimization approach to stability analysis of linear systems with interval time-varying delay by using the delay partitioning-based Lyapunov–Krasovskii Functionals (LKFs). Novel LKFs are introduced with matrices that depend on the time delays. These functionals allow the derivation of stability conditions that depend on both the upper and lower bounds on delay derivatives.