不确定变时滞系统的一个时滞相关稳定性判据

本文讨论不确定变时滞系统的稳定性问题.基于一个新的Lyapunov泛函,并利用一种新的方法处理不确定项,得到了不确定变时滞系统的一个时滞相关的稳定性判据,并利用矩阵不等式的形式给出该判据.与已有文献相比较,所得结论允许时滞导数(?)(t)(?)1且具有较少的限制条件,因此具有较弱的保守性.最后,通过两个例子验证了所给结论的正确性.     

不确定随机时滞系统的时滞相关鲁棒镇定

研究一类不确定随机时滞系统的时滞相关鲁棒镇定问题.通过引入参数化的中立型模型变换,构造Lyapunov-krasovskii泛函,运用线性矩阵不等式方法,得到了使得闭环系统为均方指数稳定的保守性较小的时滞相关鲁棒镇定条件.     

线性时滞系统的时滞相关稳定性分析

对于存在状态时滞的线性时滞系统,分为固定时滞及时变时滞两种情形,基于Lyapunov-Krasovskii理论分析稳定性,通过时滞划分,得到以LMI形式给出的一种保守性小的渐近稳定性条件,且能够处理任意变化的变时滞问题.实例表明只需粗略划分就能大大提高保守性能,为了兼顾计算负担,r取较小数值即可.并且LMI中的决策变量少,形式简洁.     

一类非线性时滞系统与时滞相关的H_∞控制

考虑一类非线性时滞系统的H∞控制.并对非线性项给出了一个新假设,在其假设下利用线性矩阵不等式方法得到了与时滞相关的H∞控制,同时也得到了该类非线性时滞系统鲁棒镇定的充分条件.     

具有离散时滞和分布时滞的中立型时滞系统的鲁棒稳定性

本文研究了具有离散时滞和分布时滞的不确定中立型系统的鲁棒稳定性的问题,考查了可能随时间变化的具有范数有界的不确定性.在对Lyapunov-Krasovskii泛函求导数时,不进行放大估计,而通过引入恰当的零项,构造线性矩阵不等式,从而获得基于LMI的时滞相关稳定的新判据.最后的数值例子说明了所得的结论有效性.     

棉田生态系统时滞动力学模型及其应用

以棉田生态系统能量流动分析为基础,建立了作物-害虫-天敌-微生物的时滞种群动力学模型,利用泛函微分方程理论对该系统进行了持久性和稳定性研究,对系统解的正性、持久性、正平衡点的存在性及全局渐近稳定性给出了相关条件,证明该系统的时滞是无害时滞.最后使用MATLAB软件对模型进行了动态模拟,对正平衡点的存在性条件和稳定性进行了验证.     

非线性随机时滞系统的时滞反馈鲁棒H∞控制

本文研究了具有变时滞的非线性随机时滞系统的时滞反馈鲁棒H∞控制问题.利用时滞分割技术,构造了新的Lyapunov-Krasovskii泛函,通过Ito公式,以线性矩阵不等式(LMI)的形式给出了时滞反馈鲁棒H∞控制器存在的充分条件,通过数值仿真算例说明了结论的正确性和方法的有效性.     

一类非线性时滞系统的时滞相关镇定及跟踪控制问题

本文讨论了一类满足Lipschitz条件的非线性时滞系统的镇定与跟踪控制问题.基于非线性状态反馈控制器,利用Lyapunov-Krasovskii泛函和矩阵理论,得到了系统时滞相关全局渐近镇定的新判据,并且保证了输出和状态跟踪控制的误差全局渐近收敛于零.本文推广了文献[9]所得到的结论.因此,本文所研究的模型及所给出的判定条件更具有一般性和实用性.     

中立型时滞系统的稳定性改进判据

研究了含有时变时滞的不确定中立系统的时滞相关稳定性问题.假定不确定参数是范数有界的,通过构造新的Lyapunov泛函和使用更一般的时滞分解方法,得到了基于LMI新颖的时滞相关稳定条件,并且用Matlab LMI工具箱很容易地求解.数值实例表明本文方法所得结果优于现有文献中的结果.     

多时滞环形神经网络系统的与时滞相关和与时滞无关的稳定性分析

本文对具有两个时滞的双向环形神经网络系统进行了稳定性分析.首先将系统在平凡解附近进行线性化处理,并得到线性化系统的特征方程,通过因式分解法,将系统的特征方程分解为四个一阶因子.其次,当系统参数在各种不同取值的情形下,通过构造辅助函数讨论了每个因子的零点均为负实部的条件,建立了与时滞相关及与时滞无关的稳定性结论.最后,本...     

一类二阶时滞微分方程在控制系统中的应用

基于时滞微分方程稳定性理论,针对一类状态向量中含有时滞的控制系统,研究其时滞相关稳定性问题.通过构造Lyapunov函数,获得了系统稳定、分岔的时滞相关充分条件,所得结论推广和改进了某些已有文献的相应结果.且借助实例及仿真结果解释所得结果的有效性.     

含非线性扰动的变时滞中立系统时滞相关稳定性新条件

研究一类含非线性扰动和混合时变时滞的中立型系统时滞相关鲁棒稳定性问题.通过构造包含三重积分项的Lyapunov-Krasovskii的泛函,结合积分不等式和自由权矩阵技术,建立了基于线性矩阵不等式(LMI)形式的离散时滞和中立时滞均相关的稳定性新判据.判据扩大了系统稳定所允许的最大时滞上界范围,具有更低的保守性.利用MATLAB的LMI工具箱进行了数值仿真,仿真算例验证了所提出的稳定性判据的有效性.     

Linear Matrix Inequality Optimization Approach to Exponential Robust Filtering for Switched Hopfield Neural Networks

This paper is concerned with the delay-dependent exponential robust filtering problem for switched Hopfield neural networks with time-delay. A new delay-dependent switched exponential robust filter is proposed that results in an exponentially stable filtering error system with a guaranteed robust performance. The design of the switched exponential robust filter for these types of neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated using standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed filter.     

Improved delay-dependent stability criteria for continuous system with two additive time-varying delay components

This paper investigated the problem of improved delay-dependent stability criteria for continuous system with two additive time-varying delay components. Free weighting matrices and convex combination method are not involved, which achieves much less numbers of linear matrix inequalities (LMIs) and LMIs scalar decision variables. By taking advantage of integral inequality and new Lyapunov–Krasovskii functional, new less conservative delay-dependent stability criterion is derived. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

New filter design for linear time-delay systems

This paper develops new robust delay-dependent filter design for a class of linear systems with time-varying delays and convex-bounded parameter uncertainties. The design procedure hinges upon the constructive use of an appropriate Lyapunov functional plus a free-weighting matrices in order to exhibit the delay-dependent dynamics. The developed approach utilizes smaller number of LMI decision variables thereby leading to less conservative solutions to the delay-dependent stability and filtering problems. Subsequently, linear matrix inequalities (LMIs)-based conditions are characterized such that the linear delay system is robustly asymptotically stable with an γ-level L₂-gain. All the developed results are tested on representative examples.     

基于改进型Bessel-Legendre不等式的电力系统时滞相关鲁棒稳定性研究

基于改进型Bessel-Legendre不等式方法,探讨了电力系统时滞相关鲁棒稳定性问题.首先构建了含有时滞环节的电力系统数学模型表达式,并推广出其含有不确定参数的模型表达式,通过应用时滞系统理论分析方法,有效地处理了泛函导数中的积分项,从而推导出了一个具有更小保守性的电力系统时滞相关鲁棒稳定新判据.通过三个数值实例对仿真结果进行了对比与验证,结果表明推导出的新判据具有有效性与优越性.     

A new augmented Lyapunov-Krasovskii functional approach for stability of linear systems with time-varying delays

This paper proposes improved delay-dependent conditions for asymptotic stability of linear systems with time-varying delays. The proposed method employs a suitable Lyapunov-Krasovskii’s functional for new augmented system. Based on Lyapunov method, delay-dependent stability criteria for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various optimization algorithms. Three numerical examples are included to show that the proposed method is effective and can provide less conservative results.     

不确定时滞系统的时滞相关非脆弱鲁棒[[H_infty]]控制

讨论了不确定时滞系统非脆弱控制器设计问题.利用Lyapunov-Krasovskii稳定性理论和最近建立的积分不等式方法,获得了不确定时滞系统在非脆弱控制器作用下不仅内部渐近稳定,而且具有给定的H∞扰动抑制水平γ的时滞相关条件.然后,针对控制器具有加法不确定性和乘法不确定性两种情况,分别给出了非脆弱控制器的设计方法,这一方法不需要调节参数,利用Matlab的LMI工具箱求解方便,数值仿真实例说明该方法的有效性.     

Robust Stability and Stabilization of a Class of Nonlinear Switched Discrete-Time Systems with Time-Varying Delays

In this paper, we investigate the problems of robust delay-dependent ℒ₂ gain analysis and feedback control synthesis for a class of nominally-linear switched discrete-time systems with time-varying delays, bounded nonlinearities and real convex bounded parametric uncertainties in all system matrices under arbitrary switching sequences. We develop new criteria for such class of switched systems based on the constructive use of an appropriate switched Lyapunov-Krasovskii functional coupled with Finsler’s Lemma and a free-weighting parameter matrix. We establish an LMI characterization of delay-dependent conditions under which the nonlinear switched delay system is robustly asymptotically stable with an ℒ₂-gain smaller than a prescribed constant level. Switched feedback schemes, based on state measurements, output measurements or by using dynamic output feedback, are designed to guarantee that the corresponding switched closed-loop system enjoys the delay-dependent asymptotic stability with an ℒ₂ gain smaller than a prescribed constant level. All the developed results are expressed in terms of convex optimization over LMIs and tested on representative examples.     

Novel delay-dependent asymptotic stability criteria for neural networks with time-varying delays

The problem of delay-dependent asymptotic stability criteria for neural networks (NNs) with time-varying delays is investigated. An improved linear matrix inequality based on delay-dependent stability test is introduced to ensure a large upper bound for time-delay. A new class of Lyapunov function is constructed to derive a novel delay-dependent stability criteria. Finally, numerical examples are given to indicate significant improvement over some existing results.