Global asymptotic stability of FAST TCP in the presence of link dynamics

We propose a continuous-time model to describe a single-link single-source network with the FAST TCP source. The proposed model explicitly includes both the queuing delay dynamics for the link dynamics and the time-varying network feedback delay. Based on the proposed model, we establish a sufficient condition for the global asymptotic stability of the FAST TCP network. We prove the sufficient condition by constructing two sequences that represent the variations of the lower and upper bound of the source’s congestion window with respect to time, and by showing that the two sequences converge to the equilibrium point of the congestion window. The simulation results illustrate the validity of the sufficient condition for the global asymptotic stability.     

On the stability of fuzzy systems

Studies the global asymptotic stability of a class of fuzzy systems. It demonstrates the equivalence of stability properties of fuzzy systems and linear time invariant (LTI) switching systems. A necessary and sufficient condition for the stability of such systems are given, and it is shown that under the sufficient condition, a common Lyapunov function exists for the LTI subsystems. A particular case when the system matrices can be simultaneously transformed to normal matrices is shown to correspond to the existence of a common quadratic Lyapunov function. A constructive procedure to check the possibility of simultaneous transformation to normal matrices is provided     

Frequency sweeping tests for stability independent of delay

In this paper we study the stability properties of linear time-invariant delay systems given in a state space form. We consider specifically the notion of asymptotic stability independent of delay. Systems with both commensurate and noncommensurate delays are investigated. We present for each class of systems a necessary and sufficient condition in terms of structured singular values, and further we demonstrate how these conditions may be extended to study stability independent of delay for uncertain systems. Our results consist of several frequency sweeping tests that can be systematically implemented and that should complement the previous work     

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.     

Average dwell time based stability analysis for nonautonomous continuous‐time switched systems

Inspired by the idea of multiple Lyapunov functions and the average dwell time, we address the stability analysis of nonautonomous continuous‐time switched systems. First, we investigate nonautonomous continuous‐time switched nonlinear systems and successively propose sufficient conditions for their (uniform) stability, global (uniform) asymptotic stability, and global (uniform) exponential stability, in which an indefinite scalar function is utilized to release the nonincreasing requirements of the classical multiple Lyapunov functions. Afterwards, by using multiple Lyapunov functions of quadratic form, we obtain the corresponding sufficient conditions for (uniform) stability, global (uniform) asymptotic stability, and global exponential stability of nonautonomous switched linear systems. Finally, we consider the computation issue of our current results for a special class of nonautonomous switched systems (ie, rational nonautonomous switched systems), associated with two illustrative examples.     

Stability of a class of switched stochastic nonlinear systems under asynchronous switching

The stability of a class of switched stochastic nonlinear retarded systems with asynchronous switching controller is investigated. By constructing a virtual switching signal and using the average dwell time approach incorporated with Razumikhin-type theorem, the sufficient criteria for pth moment exponential stability and global asymptotic stability in probability are given. It is shown that the stability of the asynchronous stochastic systems can be guaranteed provided that the average dwell time is sufficiently large and the mismatched time between the controller and the systems is sufficiently small. This result is then applied to a class of switched stochastic nonlinear delay systems where the controller is designed with both state and switching delays. A numerical example illustrates the effectiveness of the obtained results.     

具有有界输入的网络控制系统时延独立稳定性

基于有界时延、无数据包丢失、传感器时钟驱动、执行器事件驱动,文章提出了用一个特定的实值函数来调节动态输出反馈控制器的输出以确保控制对象输入有界的方法,建立了具有分布时延、有界输入、动态输出反馈网络控制系统的非线性数学模型.用李雅普诺夫第二方法和线性矩阵不等式描述分析了系统的渐近稳定性,并推导出与时延无关的系统渐近稳定的充分条件.最后MATLAB仿真算例说明：稳定判据是可行的,有界输入的控制方法是有效的.     

A dissipative dynamical systems approach to stability analysis of time delay systems

In this paper the concepts of dissipativity and the exponential dissipativity are used to provide sufficient conditions for guaranteeing asymptotic stability of a time delay dynamical system. Specifically, representing a time delay dynamical system as a negative feedback interconnection of a finite‐dimensional linear dynamical system and an infinite‐dimensional time delay operator, we show that the time delay operator is dissipative with respect to a quadratic supply rate and with a storage functional involving an integral term identical to the integral term appearing in standard Lyapunov–Krasovskii functionals. Finally, using stability of feedback interconnection results for dissipative systems, we develop sufficient conditions for asymptotic stability of time delay dynamical systems. The overall approach provides a dissipativity theoretic interpretation of Lyapunov–Krasovskii functionals for asymptotically stable dynamical systems with arbitrary time delay. Copyright © 2004 John Wiley & Sons, Ltd.     

Global asymptotic stability of delay BAM neural networks with impulses via nonsmooth analysis

In this paper, we study global asymptotic stability of delay bi-directional associative memory (BAM) neural networks with impulses. We obtain a sufficient condition of ensuring existence and uniqueness of equilibrium point for delay BAM neural networks with impulses basing on nonsmooth analysis. And we give a criteria of global asymptotic stability of the unique equilibrium point for delay BAM neural networks with impulses using Lyapunov method. At last, we present examples to illustrate that our results are feasible.     

A condition for the stability of switched nonlinear systems

In this paper, we present a sufficient condition for the global asymptotic stability of a switched nonlinear system composed of a finite family of subsystems. We show that the global asymptotic stability of each subsystem and the pairwise commutation of the vector fields that define the subsystems (i.e., the Lie bracket of any pair of them is zero) are sufficient for the global asymptotic stability of the switched system. We also show that these conditions are sufficient for the existence of a common Lyapunov function.     

Effect of transmission delay on the rate of convergence of a classof nonlinear contractive dynamical systems

We investigate the qualitative properties of a general class of contractive dynamical systems with time delay by using a unified analysis approach for any p-contraction with p in [1,infinity]. It is proved that the delayed contractive dynamical system is always globally exponentially stable no matter how large the time delay is, while the rate of convergence of the delayed system is reduced as the time delay increases. A lower bound on the rate of convergence of the delayed contractive dynamical system is obtained, which is the unique positive solution of a nonlinear equation with three parameters, namely, the time delay, the time constant and the p-contraction constant in the system. We show that the previously established results in the literature about the global asymptotic or exponential stability independent of delay for Hopfield-type neural networks can actually be deduced by recasting the network model into the general framework of contractive dynamical systems with some p-contraction (p in [1,infinity]) under the given delay-independent stability conditions. Numerical simulation examples are also presented to illustrate the obtained theoretical results.     

Stability properties of equilibria of classes of cooperativesystems

This note deals with the constant control problem for homogeneous cooperative and irreducible systems. These systems serve as models for positive systems. A necessary and sufficient condition for global asymptotic stability of the zero solution of this class of systems is known. Adding a constant control allows to shift the equilibrium point from zero to a point in the first orthant. We prove that for every nontrivial nonnegative control vector a unique nontrivial equilibrium point is achieved which is globally asymptotically stable if the zero solution of the uncontrolled system is globally asymptotically stable. In addition a converse result is provided. Finally a stability result for a particular class of Kolmogorov systems is established. We compare our main results to those in the literature     

Global asymptotic stabilisation of non-linear systems

In this article, the problem of global asymptotic stabilisation of non-linear systems is considered. First of all, the global asymptotic stability of a class of non-linear systems is considered. It is proved that the class of non-linear systems is globally asymptotically stable under certain appropriate conditions. Secondly, based on the result obtained, the global asymptotic stabilisation of a class of non-linear systems is investigated, and the feedback control laws, which globally stabilise the class of systems, are designed. Thirdly, by the coordinate change and the results obtained, the global stabilisation of the affine non-linear systems are studied, and then some sufficient conditions of stabilisation are presented. Finally, the global asymptotic stabilisation of partially linear cascade non-linear system is considered. The sufficient conditions of global stabilisation are obtained, and the corresponding feedback control laws, which stabilise the non-linear systems, are designed. In addition, some examples are given to show the effectiveness of the new results.     

一类具有时滞的广义Hopf ield 神经网络的全局稳定性

通过引入能量泛函，分析了一类具有时滞的广义Hopfield神经网络的全局稳定性．从理论上给出了该类网络为全局稳定的充分条件，证明了当时滞满足一个可计算的边界条件时，具有时滞的该类神经网络与相应的无时滞网络具有同样的全局稳定特性．仿真结果进一步证明了结论的有效性。     

Stability analysis and controller synthesis for discrete linear time-delay systems with state saturation nonlinearities

The problem of global asymptotic stability analysis and controller synthesis for a class of discrete linear time-delay systems with state saturation nonlinearities is investigated. With the introduction of a free matrix whose infinity norm is less than or equal to 1, the state of discrete linear time-delay systems with state saturation is bounded by a convex hull, which makes it feasible to apply a suitable Lyapunov functional to obtain a sufficient condition for global asymptotic stability. It is also shown that this condition can be extended to controller synthesis and discrete time-delay systems with partial state saturation. The obtained results are expressed in terms of matrix inequalities that can be solved by the presented iterative linear matrix inequality approach. The effectiveness of these results is demonstrated by some numerical examples.     

Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties

In this paper, we consider discrete time systems with polytopic time varying uncertainty. We look for a class of parameter dependent Lyapunov functions which are quadratic on the system state and depend in a polytopic way on the uncertain parameter. We show that extending the new discrete time stability condition proposed by de Oliveira et al. (Systems Control Lett. 36 (1999) 135.) to the case of time varying uncertainty leads to a necessary and sufficient condition for the computation of such a Lyapunov function. This allows to check asymptotic stability of the system under study. The obtained linear matrix inequalities condition can also be used to cope with the control synthesis problem.     

On the asymptotic stability of a particular class of distributed parameter feedback control systems†

In this paper the stability problem for a particular class of non-linear feedback control systems governed by a parabolic partial differential equation is considered. A sufficient condition for global asymptotic stability of the null equilibrium state is derived by the method of comparison functions.     

基于自由权矩阵法的网络控制系统稳定性研究

研究了包含随机、有界传输时延和丢包的网络控制系统的稳定。将网络控制系统建模为具有时变输入时延的离散时间模型,利用Lyapunov-Krasovskii定理和自由权矩阵法,推导得出基于线性矩阵不等式形式的渐近稳定充分条件。数值仿真验证了方法的有效性。