离散区间二型Tagaki-Sugeno模型时滞系统广义耗散控制设计

对带有时变时滞和外部扰动的一类离散区间二型Tagaki-Sugeno(T–S)模型非线性系统,研究了其广义耗散性能分析与状态反馈控制器的设计问题.与一型T–S模糊系统相比,区间二型模糊系统能更好地处理隶属函数中的不确定信息.首先,通过模型转换的方法,对系统的滞后状态进行变换,从而将时变时滞的不确定性从原系统中分离出.根据转换后的仅含定常时滞和具有有界误差范数的两个子系统,利用时滞依赖的李雅普诺夫-克拉索夫斯基泛函方法推导出了使系统渐近稳定并具有广义耗散性能的充分条件.接着,设计了保证闭环系统渐近稳定并具有广义耗散性能指标的状态反馈控制器.最后由数值仿真验证了设计方法的有效性.     

Extended dissipativity of generalised neural networks including time delays

This article explores the extended dissipativity conditions for generalised neural networks (GNNs) including interval time-varying delays. Extended dissipativity criterions are proposed by making proper Lyapunov–Krasovskii functional. The improved reciprocally convex combination and weighted integral inequality techniques are together applied in main results to establish the new extended dissipativity conditions of delayed GNNs. Finally, the feasibility and superiority of the proposed novel approach is clearly shown by numerical examples.     

(<Emphasis Type="Italic">m</Emphasis>,<Emphasis Type="Italic">N</Emphasis>)-delay-partitioning approach to stability analysis for T-S fuzzy systems with interval time-varying delay

This paper is concerned with improved stability criteria for uncertain T-S fuzzy systems with interval time-varying delay by means of a new (m,N)-delay-partitioning approach. Based on an appropriate augmented LKF established in the framework of state vector augmentation, some tighter bounding inequalities (Seuret-Wirtinger’s integral inequality, Peng-Park’s integral inequality and the reciprocally convex approach) have been employed to deal with (time-varying) delay-dependent integral items of the derivative of LKF, therefore, less conservative delaydependent stability criteria can be obtained on account of none of any useful time-varying items are arbitrarily ignored. It’s worth mentioning that, when the delay-partitioning number m is fixed, less conservatism can be achieved by increase of another delay-partitioning number N, but without increasing any computing burden. Finally, one numerical example is provided to show that the proposed conditions are less conservative than existing ones.     

Robust stability of interval bidirectional associative memory neural network with time delays.

In this paper, the conventional bidirectional associative memory (BAM) neural network with signal transmission delay is intervalized in order to study the bounded effect of deviations in network parameters and external perturbations. The resultant model is referred to as a novel interval dynamic BAM (IDBAM) model. By combining a number of different Lyapunov functionals with the Razumikhin technique, some sufficient conditions for the existence of unique equilibrium and robust stability are derived. These results are fairly general and can be verified easily. To go further, we extend our investigation to the time-varying delay case. Some robust stability criteria for BAM with perturbations of time-varying delays are derived. Besides, our approach for the analysis allows us to consider several different types of activation functions, including piecewise linear sigmoids with bounded activations as well as the usual C1-smooth sigmoids. We believe that the results obtained have leading significance in the design and application of BAM neural networks.     

Dissipativity analysis of complex-valued BAM neural networks with time delay

Neural Computing and Applications - This paper is concerned with dissipativity analysis of complex-valued bidirectional associative memory (BAM) neural networks (NNs) with time delay. Some novel...     

时变时滞神经网络的时滞相关鲁棒稳定性和耗散性分析

研究时变时滞神经网络的鲁棒稳定性和耗散性问题.充分利用积分项的时滞信息和激励函数条件构造一个合适的增广LK泛函;利用自由矩阵积分不等式处理LK泛函的导数,得到一个低保守性的时滞相关稳定判据;将所获得的结论延伸至神经网络的耗散性分析,并推导出一个确保神经网络严格$(\mathcalX, \mathcalY,\mathcalZ)-\gamma$-耗散的充分条件.最后通过3个数值算例验证了所提出方法的可行性和优越性.     

Global Dissipativity of Inertial Neural Networks with Proportional Delay via New Generalized Halanay Inequalities

This article is devoted to the global dissipativity of inertial neural networks with proportional delay. A novel generalized Halanay inequality which involves proportional delay is established. By constructing a new generalized Halanay inequality, several new explicit delay-independent conditions are derived in terms of linear matrix inequalities to ensure the global dissipativity of the considered system. Moreover, a new differential delay inequality which involves unbounded time-varying delay is considered. Due to the proportional delay is one type of unbounded time-varying delays, new analysis techniques can effectively avoid the difficulties caused by proportional delay by applying a new differential delay inequality. Especially, several novel delay-dependent sufficient conditions are obtained to guarantee the global dissipativity of the considered system. Finally, two simulations examples are provided to illustrate the validity of the proposed theoretical analysis.     

New stability criteria for BAM neural networks with time-varying delays

In this paper, the exponential stability is investigated for a class of time-delay BAM neural networks (NNs). Time delays of two layers are taken into account separately rather than as a whole with the idea of delay fractioning. Then we generalize the result to time-varying interval delay condition. Exploiting the known constant part of delay sufficiently to estimate the upper bounds, we can derive an improved stability for BAM NNs with time-varying interval delay. Two examples are provided to demonstrate the less conservatism and effectiveness of the proposed linear matrix inequality (LMI) conditions.     

Delay-derivative-dependent stability criterion for neural networks with probabilistic time-varying delay

In this article, based on Lyapunov–Krasovskii functional approach and improved delay-partitioning idea, a new sufficient condition is derived to guarantee a class of delayed neural networks to be asymptotically stable in the mean-square sense, in which the probabilistic time-varying delay is addressed. Together with general convex combination method, the criterion is presented via LMIs and its solvability heavily depends on the sizes of both time delay range and its derivative, which has wider application fields than those present ones. It can be shown by the numerical examples that our method reduces the conservatism much more effectively than earlier reported ones. Especially, the conservatism can be further decreased by thinning the delay intervals.     

Impulsive effect on global exponential stability of BAM fuzzy cellular neural networks with time-varying delays

In this article, a class of impulsive bidirectional associative memory (BAM) fuzzy cellular neural networks (FCNNs) with time-varying delays is formulated and investigated. By employing delay differential inequality and M-matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM FCNNs with time-varying delays are obtained. In particular, a precise estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive perturbation intention. It is believed that these results are significant and useful for the design and applications of BAM FCNNs. An example is given to show the effectiveness of the results obtained here.     

Delay-partitioning approach to stability analysis of state estimation for neutral-type neural networks with both time-varying delays and leakage term via sampled-data control

This paper mainly focuses on further improved stability analysis of state estimation for neutral-type neural networks with both time-varying delays and leakage delay via sampled-data control by delay-partitioning approach. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states and a sampled-data estimator is constructed. To fully use the sawtooth structure characteristics of the sampling input delay, sufficient conditions are derived such that the system governing the error dynamics is asymptotically stable. The design method of the desired state estimator is proposed. We construct a suitable Lyapunov–Krasovskii functional (LKF) with triple and quadruple integral terms then by using a novel free-matrix-based integral inequality (FMII) including well-known integral inequalities as special cases. Moreover, the design procedure can be easily achieved by solving a set of linear matrix inequalities (LMIs), which can be easily facilitated by using the standard numerical software. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed results.     

Dissipativity of extended Pouzet–Runge–Kutta methods for neutral delay integro-differential equations

This paper is concerned with dissipativity of extended Pouzet–Runge–Kutta methods for neutral delay integro-differential equations. The finite-dimensional and infinite-dimensional dissipativity results of the (k, l)-algebraically stable extended Pouzet–Runge–Kutta methods are obtained under suitable conditions.     

混合时滞不确定中立系统鲁棒稳定的时滞分割方法

研究了一类同时具有离散与分布时滞的不确定中市型系统的鲁棒稳定性问题.基于时滞分割思想,通过构造一类特殊的Lyapunov-Krasovskii泛函,并利用Jensen不等式,建立了线性矩阵不等式形式的时滞相关鲁棒稳定性新判据.该方法不涉及模型变换与自由权矩阵技术,减少了理论与计算上的复杂性;同时允许中立时滞项的系数矩阵...     

Periodic Dynamics for Memristor-based Bidirectional Associative Memory Neural Networks with Leakage Delays and Time-varying Delays

This paper deals with a class of memristor-based bidirectional associative memory (BAM) neural networks with leakage delays and time-varying delays. With the aid of the framework of Filippov solutions, Chain rule and some inequality techniques, a sufficient condition which ensures the boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks with leakage delays and time-varying delays is established. Applying a new approach involving Yoshizawa-like theorem, we prove the existence of periodic solution of the memristor-based BAM neural networks. By using the theory of set-valued maps and functional differential inclusions, Lyapunov functional, a set of sufficient conditions which guarantee the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks are derived. An example is given to illustrate the applicability and effectiveness of the theoretical predictions. The results obtained in this paper are completely new and complement the previously known studies of Li et al. [Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays, Neural networks 75 (2016) 97-109.]     

Dissipative control for state-saturated discrete time-varying systems with randomly occurring nonlinearities and missing measurements

In this paper, the dissipative control problem is investigated for a class of discrete time-varying systems with simultaneous presence of state saturations, randomly occurring nonlinearities as well as multiple missing measurements. In order to render more practical significance of the system model, some Bernoulli distributed white sequences with known conditional probabilities are adopted to describe the phenomena of the randomly occurring nonlinearities and the multiple missing measurements. The purpose of the addressed problem is to design a time-varying output-feedback controller such that the dissipativity performance index is guaranteed over a given finite-horizon. By introducing a free matrix with its infinity norm less than or equal to 1, the system state is bounded by a convex hull so that some sufficient conditions can be obtained in the form of recursive nonlinear matrix inequalities. A novel controller design algorithm is then developed to deal with the recursive nonlinear matrix inequalities. Furthermore, the obtained results are extended to the case when the state saturation is partial. Two numerical simulation examples are provided to demonstrate the effectiveness and applicability of the proposed controller design approach.     

Stochastic dissipativity analysis on discrete-time neural networks with time-varying delays

In this paper, the problems of global dissipativity and global exponential dissipativity are investigated for discrete-time stochastic neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing stochastic analysis technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequalities (LMIs). Furthermore, when the parameter uncertainties appear in the discrete-time stochastic neural networks with time-varying delays, the delay-dependent robust dissipativity criteria are also presented. Two examples are given to show the effectiveness and less conservatism of the proposed criteria.     

Robust stability of uncertain fuzzy Cohen–Grossberg BAM neural networks with time-varying delays

In this paper, the Takagi–Sugeno (TS) fuzzy model representation is extended to the stability analysis for uncertain Cohen–Grossberg type bidirectional associative memory (BAM) neural networks with time-varying delays using linear matrix inequality (LMI) theory. A novel LMI-based stability criterion is obtained by using LMI optimization algorithms to guarantee the asymptotic stability of uncertain Cohen–Grossberg BAM neural networks with time varying delays which are represented by TS fuzzy models. Finally, the proposed stability conditions are demonstrated with numerical examples.     

Robust extended dissipativity criteria for discrete-time uncertain neural networks with time-varying delays

In this draft, we consider the problem of robust extended dissipativity for uncertain discrete-time neural networks (DNNs) with time-varying delays. By constructing appropriate Lyapunov–Krasovskii functional (LKF), sufficient conditions are established to ensure that the considered time-delayed uncertain DNN is extended dissipative. The derived conditions are presented in terms of linear matrix inequalities (LMIs). Numerical examples are provided to illustrate the superiority of this result.

     

LESO-based Position Synchronization Control for Networked Multi-Axis Servo Systems With Time-Varying Delay

The position synchronization control (PSC) problem is studied for networked multi-axis servo systems (NMASSs) with time-varying delay that is smaller than one sampling period. To improve the control performance of the system, time-varying delays, modeling uncertainties, and external disturbances are first modeled as a lumped disturbance. Then, a linear extended state observer (LESO) is devised to estimate the system state and the lumped disturbance, and a linear feedback controller with disturbance compensation is designed to perform individual-axis tracking control. After that, a cross-coupled control approach is used to further improve synchronization performance. The bounded-input-bounded-output (BIBO) stability of the closed-loop control system is analyzed. Finally, both simulation and experiment are carried out to demonstrate the effectiveness of the proposed method.      

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.