Asymptotic Stability of Cohen–Grossberg BAM Neutral Type Neural Networks with Distributed Time Varying Delays

This paper is concerned with the problem of asymptotic stability of neutral type Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays. By constructing a suitable Lyapunov–Krasovskii functional (LKF), reciprocal convex technique and Jensen’s inequality are used to delay-dependent conditions are established to analysis the asymptotic stability of Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays. These stability conditions are formulated as linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms. Finally numerical examples are given to illustrate the usefulness of our proposed method.     

Delay-dependent robust stabilisation for a class of fuzzy bilinear systems with time-varying delays in state and control input

The stabilisation problem for a class of Takagi–Sugeno (TS) fuzzy bilinear systems (FBSs) with time-varying state and input delays is investigated in this article. A fuzzy controller is designed to stabilise TS FBSs with time-varying state and input delays via the parallel distributed compensation method. Based on a Lyapunov–Krasoviskii function, the delay-dependent stabilisation conditions are proposed in terms of a linear matrix inequality to guarantee the asymptotic stabilisation of time-delay FBSs with disturbance input. Two numerical examples with delays in the state and input are given to demonstrate that the proposed stability condition is less conservative than some existing results. Finally, the validity and applicability of the proposed control scheme are successfully demonstrated in the control of a Van de Vusse reactor with delay.     

On the stability of uncertain systems with multiple time-varyingdelays

In this paper, criteria for the global asymptotic stability of a class of uncertain systems with multiple time-varying delays are proposed. Based on the improved Razumikhin-type theorem, delay-dependent and delay-independent criteria are provided to guarantee the global asymptotic stability of such systems. Our main results are generalizations of some recent results reported in the literature in the case with multiple time-varying delays. A numerical example Is also given to illustrate our results     

Existence and global asymptotic stability of periodic solution for discrete and distributed time-varying delayed neural networks with discontinuous activations

In this paper, we study a general class of neural networks with discrete and distributed time-varying delays, whose neuron activations are discontinuous and may be unbounded or nonmonotonic. By using the Leray-Schauder alternative theorem in multivalued analysis, matrix theory and generalized Lyapunov-like approach, we obtain some sufficient conditions ensuring the existence, uniqueness and global asymptotic stability of the periodic solution. Moreover, when all the variable coefficients and time delays are real constants, we discuss the global convergence in finite time of the neural network dynamical system. Our results extend previous works not only on discrete and distributed time-varying delayed neural networks with continuous or even Lipschitz continuous activations, but also on discrete and distributed time-varying delayed neural networks with discontinuous activations. Two numerical examples are given to illustrate the effectiveness of our main results.     

Robust H∞ control of uncertain stochastic Markovian jump systems with mixed time-varying delays

In this paper, robust H_∞ control for a class of uncertain stochastic Markovian jump systems (SMJSs) with interval and distributed time-varying delays is investigated. The jumping parameters are modelled as a continuous-time, finite-state Markov chain. By employing the Lyapunov-Krasovskii functional and stochastic analysis theory, some novel sufficient conditions in terms of linear matrix inequalities are derived to guarantee the mean-square asymptotic stability of the equilibrium point. Numerical simulations are given to demonstrate the effectiveness and superiority of the proposed method comparing with some existing results.     

Analysis of distributed power control under constant and time-varying delays

This work studies the distributed power control algorithm proposed in 1993 by Foschini-Miljanic, standardised for universal mobile telecommunication systems. Continuous and discrete time versions of this algorithm are analysed. First, the stability of the distributed power allocation schemes was studied, where sufficient conditions to guarantee stability and convergence to a desired quality of service were provided. In this study, the channel gains are assumed to be slowly time-varying or piece-wise constant. For closed-loop control, a proportional controller is then employed under integral action in order to achieve good tracking despite time-varying and unknown channel gains. Next, the effects of constant and time-varying time delays in the closed-loop structure are studied. Explicit stability regions for the control gains in the Foschini-Miljanic scheme are derived for both the continuous and discrete-time versions of the algorithm, under constant and time-varying delays. For time-varying scenario, the resulting stability regions do not impose limitations on the rate change of the time-varying profiles. A comprehensive evaluation using simulations is performed to validate the analytical derivations described in the paper.     

Enhancement on stability criteria for linear systems with interval time-varying delays

In this paper, the problem of stability for linear systems with interval time-varying delays is investigated. By constructing a suitable augmented Lyapunov-Krasovskii functional and utilizing Wirtinger-based integral inequality, two sufficient conditions for guaranteeing the asymptotic stability of the concerned systems are derived within the framework of linear matrix inequalities (LMIs). The superiority and validity of the proposed criteria are verified by comparing maximum delay bounds under various conditions via two numerical examples.     

Robust stability of stochastic genetic regulatory networks with discrete and distributed delays

In this paper, the problem on asymptotical and robust stability of genetic regulatory networks with time-varying delays and stochastic disturbance is considered. The time-varying delays include not only discrete delays but also distributed delays. The parameter uncertainties are time-varying and norm-bounded. Based on the Lyapunov stability theory and Lur’s system approach, sufficient conditions are given to ensure the stability of genetic regulatory networks. All the stability conditions are given in terms of linear matrix inequalities, which are easy to be verified. Illustrative example is presented to show the effectiveness of the obtained results.     

Sampled-data stabilization of linear time-delay systems

Sampled-data feedback control of linear systems governed by differential-difference equations is considered. The sampling introduces time-varying and discontinuous delays in the closed-loop system. A comparison method is used to derive sufficient conditions for asymptotic stability of the closed-loop system with specified exponential decay rate.     

Variable structure sliding mode control for a class of uncertain distributed parameter systems with time-varying delays

This article considers sliding mode control of a class of parabolic linear uncertain distributed parameter systems with time-varying delays. The sliding mode controller design does not contain time delay terms and drives the state trajectory of the system to the sliding manifold in finite time. A sufficient condition of asymptotic stability for the sliding motion is derived. A simulation example is presented to illustrate effectiveness of the proposed method.     

Delay-Dependent Stability for Recurrent Neural Networks With Time-Varying Delays

This brief is concerned with the stability for static neural networks with time-varying delays. Delay-independent conditions are proposed to ensure the asymptotic stability of the neural network. The delay-independent conditions are less conservative than existing ones. To further reduce the conservatism, delay-dependent conditions are also derived, which can be applied to fast time-varying delays. Expressed in linear matrix inequalities, both delay-independent and delay-dependent stability conditions can be checked using the recently developed algorithms. Examples are provided to illustrate the effectiveness and the reduced conservatism of the proposed result.      

Controller synthesis for uncertain fuzzy systems with integrating multiple time-varying delays

This article mainly investigates the controller synthesis for uncertain fuzzy systems with integrating multiple time-varying delays, which can describe a much larger class of nonlinear systems or uncertain time-delay systems. First, a sufficient stability condition for the unforced Takagi–Sugeno (T-S) fuzzy models with multiple time-varying delays and uncertainties are derived. By involving the parallel distributed compensator (PDC), some design conditions for the resulting closed-loop fuzzy systems are further presented. These proposed conditions are all expressed in terms of linear matrix inequalities (LMIs), and we can readily perform the PDC synthesis from current LMI solvers. Numerical examples are given to demonstrate the validity and superiority of the proposed approach.     

时滞项可微系统的时滞依赖的稳定性条件

本文研究了带有可微时滞项连续系统的稳定性问题. 通过利用时滞项导数的信息, 给出了改进的时滞系统渐近稳定性条件. 与已有的做法不同, 即便是时滞项导数的上界大于等于 1 时这个上界仍可被利用. 文中证明了所得结果比已有结果的保守性小. 同时, 由于涉及较少的决策变量, 计算复杂度也大为降低. 数例进一步说明了所得结果的有效性和少保守性.     

Global asymptotic stability analysis for neutral-type complex-valued neural networks with random time-varying delays

This paper investigates the global asymptotic stability problem for a class of neutral-type complex-valued neural networks with random time-varying delays. By introducing a stochastic variable with Bernoulli distribution, the information of time-varying delay is assumed to be random time-varying delays. By constructing an appropriate Lyapunov–Krasovskii functional and employing inequality technique, several sufficient conditions are obtained to ensure the global asymptotically stability of equilibrium point for the considered neural networks. The obtained stability criterion is expressed in terms of complex-valued linear matrix inequalities, which can be simply solved by effective YALMIP toolbox in MATLAB. Finally, three numerical examples are given to demonstrate the efficiency of the proposed main results.     

Stability results for stochastic bidirectional associative memory neural networks with multiple discrete and distributed time-varying delays

This paper is concerned with the global asymptotic stability of a class of stochastic bidirectional associative memory neural networks with both multiple discrete and distributed time-varying delays. A new criterion of asymptotic stability is derived in terms of linear matrix inequality, which can be efficiently solved by a standard numerical software. An illustrative numerical example is also given to show the applicability and effectiveness of the proposed results.     

线性多时变时滞系统的指数稳定性

本文基于一个新型滞后动态系统指数稳定性定理和两个准备引理, 采用 Lyapunov 函数稳定性分析新方法, 建立了线性多时变时滞系统保守性少的稳定性条件. 与文献中已有的一些结果不同, 所建立的稳定性条件不依赖于时变时滞的变化率. 因此, 所建立的结果适用于具有非常快变时滞的系统. 文中给出了一个例子展示所得结果好于直接采用标准的 Razumikhin 型条件所得的结果.     

New Delay-dependent stability criteria for neutral systems with time-varying delay using delay-decomposition approach

This paper concerns with the problem of asymptotic stability for neutral systems with timevarying delays. With the introduction of delay-decomposition approach, some new delay-dependent stability criteria are established and formulated in the form of linear matrix inequalities. Both constant time delays and time-varying delays have been taken into account. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

Teleoperation in the presence of varying time delays and sandwich linearity in actuators

In this paper, a novel control scheme is proposed to guarantee global asymptotic stability of bilateral teleoperation systems that are subjected to time-varying time delays in their communication channel and sandwich linearity in their actuators. This extends prior art concerning control of nonlinear bilateral teleoperation systems under time-varying time delays to the case where the local and the remote robots’ control signals pass through saturation or similar nonlinearities that belong to a class of systems we name sandwich linear systems. Our proposed controller is similar to the proportional plus damping (P+D) controller with the difference that it takes into account the actuator saturation at the outset of control design and alters the proportional term by passing it through a nonlinear function; thus, we call the proposed method as nonlinear proportional plus damping (nP+D). The asymptotic stability of the closed-loop system is established using a Lyapunov–Krasovskii functional under conditions on the controller parameters, the actuator saturation characteristics, and the maximum values of the time-varying time delays. To show the effectiveness of the proposed method, it is simulated on a variable-delay teleoperation system comprising a pair of planar 2-DOF robots subjected to actuator saturation. Furthermore, the controller is experimentally validated on a pair of 3-DOF PHANToM Premium 1.5A robots, which have limited actuation capacity, that form a teleoperation system with a varying-delay communication channel.     

New results for delay-dependent stability of linear systems with time-varying delay

The asymptotic stability problem for a class of linear systems with time-varying delays is studied using a generalized discretized Lyapunov functional approach. The kernel of the functional, which is a function of two variables, is chosen as piecewise linear. The conditions of the Lyapunov functional and its derivative are written in terms of linear matrix inequalities (LMIs). New delay-dependent stability criteria are proposed by simplifying the derived LMIs. Numerical examples show that the results obtained by these new criteria significantly improve the estimate of stability limit over the existing results in the literature.     

Global μ -Stability of Delayed Neural Networks With Unbounded Time-Varying Delays

In this letter, dynamical systems with unbounded time-varying delays are investigated. We address the following question: To what extent the time-varying delays can exist while the system is stable? Moreover, a new concept of stability, global mu-stability, is proposed. Under mild conditions, we prove that the dynamical systems with unbounded time-varying delays are globally mu-stable.