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 delay-range-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.

New criterion for delay-dependent absolute stability of Lurie system with interval time-varying delay

The delay-dependent absolute stability for a class of Lurie systems with interval time-varying delay is studied. By employing an augmented Lyapunov functional and combining a free-weighting matrix approach and the reciprocal convex technique, an improved stability condition is derived in terms of linear matrix inequalities （LMIs）. By retaining some useful terms that are usually ignored in the derivative of the Lyapunov function, the proposed sufficient condition depends not only on the lower and upper bounds of both the delay and its derivative, but it also depends on their differences, which has wider application fields than those of present results. Moreover, a new type of equality expression is developed to handle the sector bounds of the nonlinear function, which achieves fewer LMIs in the derived condition, compared with those based on the convex representation. Therefore, the proposed method is less conservative than the existing ones. Simulation examples are given to demonstrate the validity of the approach.

Passivity analysis for uncertain stochastic neural networks with discrete interval and distributed time-varying delays

The problem of passivity analysis is investigated for uncertain stochastic neural networks with discrete interval and distributed time-varying delays.The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belongs to a given interval,which means that the lower and upper bounds of interval time-varying delays are available.By constructing proper Lyapunov-Krasovskii functional and employing a combination of the free-weighting matrix method and stochastic analysis technique,new delay-dependent passivity conditions are derived in terms of linear matrix inequalities（LMIs）.Finally,numerical examples are given to show the less conservatism of the proposed conditions.

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

The problem of delay-dependent asymptotic stability for neurM networks with interval time-varying delay is investigated. Based on the idea of delay decomposition method, a new type of Lyapunov Krasovskii functional is constructed. Several novel delay-dependent stability criteria are presented in terms of linear matrix inequality by using the Jensen integral inequality and a new convex combination technique. Numerical examples are given to demonstrate that the proposed method is effective and less conservative.

Improved delay-dependent robust H_∞ control of an uncertain stochastic system with interval time-varying and distributed delays

In this paper, the robust H∞control problem for a class of stochastic systems with interval time-varying and distributed delays is discussed. The system under study involves parameter uncertainty, stochastic disturbance, interval time-varying,and distributed delay. The aim is to design a delay-dependent robust H∞control which ensures the robust asymptotic stability of the given system and to express it in the form of linear matrix inequalities（LMIs）. Numerical examples are given to demonstrate the effectiveness of the proposed method. The results are also compared with the existing results to show its conservativeness.

Numerical solutions of linear quadratic control for time-varying systems via symplectic conservative perturbation

Optimal control system of state space is a conservative system, whose approximate method should be symplectic conservation. Based on the precise integration method, an algorithm of symplectic conservative perturbation is presented. It gives a uniform way to solve the linear quadratic control （LQ control） problems for linear timevarying systems accurately and efficiently, whose key points are solutions of differential Riccati equation （DRE） with variable coefficients and the state feedback equation. The method is symplectic conservative and has a good numerical stability and high precision. Numerical examples demonstrate the effectiveness of the proposed method.

New Results on H_∞ Control of Linear Systems with Interval Time-Varying Delays

This paper is focused on the H_(∞) control problem for linear systems with interval timevarying delays.By employing a reciprocally convex combination approach and a delay decomposition approach,some new delay-dependent bounded real lemmas(BRLs) are derived such that the closedloop system is asymptotically stable with a prescribed H_(∞) level.The BRLs are then used to solve the H_(∞) controller design by incorporating with the cone complementary approach.Three numerical examples are finally given to show the validity of the proposed method.

Delay-dependent Non-fragile H_∞ Control for Linear Systems with Interval Time-varying Delay

This paper considers the problem of delay-dependent non-fragile H∞control for a class of linear systems with interval time-varying delay. Based on the direct Lyapunov method, an appropriate Lyapunov-Krasovskii functional(LKF) with triple-integral terms and augment terms is introduced. Then, by using the integral inequalities and convex combination technique, an improved H∞performance analysis criterion and non-fragile H∞controller are formulated in terms of linear matrix inequalities(LMIs), which can be easily solved by using standard numerical packages. At last, two numerical examples are provided to demonstrate the effectiveness of the obtained results.

灰色随机线性时滞系统的渐近稳定性

首先提出了灰色随机线性时滞系统及其渐近稳定性的概念;然后,利用矩阵理论和随机微分时滞方程解的渐近收敛定理及李雅普诺夫函数,研究了灰色随机线性时滞系统的渐近稳定性,得到了随机渐近稳定的几个充分性条件;最后,通过数值例子说明了所得结果在实际应用中的方便性和有效性.

一类网络化控制系统的局部最优控制器设计

假定延时恒定且小于1个采样周期,采用Lyapunov函数、线性矩阵不等式(LMI)以及区间矩阵的概念,对状态反馈回路网络化的控制系统控制器增益进行设计,以寻求某个局部最优控制器增益,使网络化控制系统渐近稳定并同时使该控制器增益可变区间达到最大。此局部最优控制器增益以及控制器增益的最大可变区间可以利用LMI工具箱中的求解器gevp得到。实例表明,采用此种设计方法很容易得到局部最优控制器。

区间矩阵二次稳定的充分必要条件

提出了区间矩阵二次稳定的充分必要条件,以及相应的稳定裕度的计算方法.结论以线性矩阵不等式(LMI)的形式给出.利用功能强大的LMI工具,求解非常方便.所给实例表明,该方法用于确定区间矩阵的鲁棒稳定性及其稳定裕度,非常有效.

灰色随机线性系统的均方鲁棒稳定性

给出了区间灰色伊藤随机线性系统及其均方鲁棒稳定的概念,在此基础上,利用矩阵特征值理论和区间灰矩阵的性质及Lyapunov函数法,研究了该系统的均方鲁棒稳定性,得到了均方鲁棒稳定的几个条件.最后,通过一个数值例子说明了这些判定条件的简洁性和有效性.

区间矩阵稳定的新充分必要条件(英文)

本文讨论了对称区间矩阵的稳定性并给出了一个简单的充分必要条件，同时还讨论了线性时变区间矩阵和非线性时变区间矩阵的稳定性．