一类时滞微分系统无条件稳定的条件

本文给出系统dx(t)/dt=a_1x(t)+a_2x(t-τ)+b_1y(t)+b_2y(t-τ),dy(t)/dt=c_1x(t)+c_2x(t-τ)+d_1y(t)+d_2y(t-τ)对任意时滞τ≥0为无条件稳定的必要与充分条件。这个问题是由A.A在1946年提出的,1960年文[2]给出了这个问题的初步结果。本文给出了这个结果的明显形式,它是在判定四次代数方程在区间[-1,1]内无实根的基础上得到的。为了工程技术人员的方便,我们也给出了这个判定的明显形式。     

关于《一类非线性时滞系统的稳定化控制器设计研究》一定理的讨论

文献[1]将精确线性化的方法应用到一类时滞非线性系统稳定化控制器设计中,提出一种新的稳定化控制器设计方法,其思路是可取的.但是我认为其中的定理1有误,下面提出一家之言与作者商讨.考虑单输入非线性时滞系统x=f(x) g(x)u(t-τ),(1)其中x∈Rn,u∈R,f(.),g(.)为C∞非线性向量场;τ为时滞,f(0)=0.同时引入线性时滞系统w=Aw bu(t-τ),(2)其中w=[w1…wn]T∈Rn为新的状态变量A=01…0?0……0,　b=0?1.(3)　　原定理为定理1.对于非线性时滞系统(1),通过微分同胚变换w=T(x)将其转化成线性时滞系统(3)的充分必要条件是(i)rankM(x)=n,其中M(…     

具有状态和控制滞后不确定系统的保性能控制器设计

1　引言本文的目的在于将文献 [1 ]的结论推广到同时具有状态和控制滞后的不确定系统 ,并进而研究其最优保性能控制问题 .考虑具有状态和控制滞后的不确定系统x( t) =[A DF( t) E1 ] x( t) [Ad DF( t) Ed] x( t-d) [B DF( t) E2 ] u( t) [Bh DF( t) Eh]《u》( t-     

线性多时滞差分微分系统全时滞稳定的代数判据

考虑下列线性多时滞差分微分系统 ?(t)=A_0x(t)+sum from k=1 to N(A_kx(t-τk·r),其中X∈R~n,A_k(k=0,1,…,N)是n×n常数矩阵;τk=(τk1,τk2,…,τkM),τkj(k=1,…,N;j=1,…,M)是整数,r~T=(r_1,r_2,…,rM),τk·r=sum from j=1 to M(τkj·rj)。本文利用Liapunov函数和Liapunov泛函,给出了系统(*)全时滞稳定的代数判别准则;并具体讨论了n=3,N=1时,系统(*)全时滞稳定的代数条件,克服了Hale文中验证“超越”条件的困难,为实际工作者提供了十分有效而方便的判别方法。     

具有多输入时滞的不确定广义系统的时滞相关鲁棒镇定

研究具有多输入时滞及参数不确定性的广义系统的时滞相关鲁棒镇定问题. 首先利用LMI给出相应的标称系统的时滞相关镇定准则. 然后, 基于这个准则, 设计状态反馈控制器, 使得对任何允许的不确定参数相应的闭环系统是正则, 稳定, 无脉冲的. 最后的数值算例表明所提方法是有效的.     

时滞线性系统(t)=Ax(t)+Bx(t-τ)稳定性的新判据

提出了(t)=Ax(t)+Bx(t-τ)时滞无关稳定的一个充分条件,并进而研究了系统在不满足时滞无关稳定条件下,不稳定特征根的区域范围,给出了一个与时滞相关稳定的新的充分条件. 文末,给出了本文结论的示例,并与已有结果进行了比较,表明了该方法的有效性和可行性.     

单滞后时变区间动力系统的指数稳定性

用矩阵测度和时滞微分不等式研究了单滞后时变区间动力系统 x(t) =N[P(t) ,Q(t) ]x(t) +N[C(t) ,D(t) ]x(t -τ) ,τ≥ 0 的指数稳定性 ,给出了其指数稳定的判别准则 ,推广和改进了文 [1～ 3]的工作     

时滞线性系统x·(t)=Ax(t)+Bx(t-τ)稳定性的新判据

提出了x·(t)=Ax(t)+Bx(t-τ)时滞 无关稳定的一个充分条件，并进而研究了系统在不满足时滞无关稳定条件下，不稳定特征根 的区域范围，给出了一个与时滞相关稳定的新的充分条件. 文末，给出了本文结论的示例， 并与已有结果进行了比较，表明了该方法的有效性和可行性.     

时滞线性系统(t)=Ax(t) Bx(t-τ)稳定性的新判据

提出了 x(t) =Ax(t) Bx(t- τ)时滞无关稳定的一个充分条件 ,并进而研究了系统在不满足时滞无关稳定条件下 ,不稳定特征根的区域范围 ,给出了一个与时滞相关稳定的新的充分条件 .文末 ,给出了本文结论的示例 ,并与已有结果进行了比较 ,表明了该方法的有效性和可行性 .     

线性时滞系统的时滞相关鲁棒控制

讨论了同时具有输入时滞与状态时滞的线性系统的时滞相关鲁棒控制问题.将矩阵分解思想应用于线性时滞系统的控制综合,借助于积分不等式,利用Lyapunov_Krasovskii泛函方法,得到了系统经无记忆状态反馈后可镇定的、基于LMI的时滞相关条件.既不要对原系统进行模型变换,也不要对交叉项进行界定.最后的实例说明了本文方法的有效性.     

Delay-dependent stabilization of linear systems with time-varying state and input delays

The integral-inequality method is a new way of tackling the delay-dependent stabilization problem for a linear system with time-varying state and input delays: . In this paper, a new integral inequality for quadratic terms is first established. Then, it is used to obtain a new state- and input-delay-dependent criterion that ensures the stability of the closed-loop system with a memoryless state feedback controller. Finally, some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective, even though neither (A,B₁) nor (A+A₁,B₁) is stabilizable.     

New results on stability and L∞‐gain analysis for positive linear differential‐algebraic equations with unbounded time‐varying delays

This article addresses the problems of stability and L_∞‐gain analysis for positive linear differential‐algebraic equations with unbounded time‐varying delays for the first time. First, we consider the stability problem of a class of positive linear differential‐algebraic equations with unbounded time‐varying delays. A new method, which is based on the upper bounding of the state vector by a decreasing function, is presented to analyze the stability of the system. Then, by investigating the monotonicity of state trajectory, the L_∞‐gain for differential‐algebraic systems with unbounded time‐varying delay is characterized. It is shown that the L_∞‐gain for differential‐algebraic systems with unbounded time‐varying delay is also independent of the delays and fully determined by the system matrices. Two numerical examples are given to illustrate the obtained results.     

Exponential H∞ filtering for nonlinear discrete‐time switched stochastic systems with mixed time delays and random missing measurements

This paper is concerned with the exponential H_∞ filtering for a class of nonlinear discrete‐time switched stochastic hybrid systems with mixed time delays and random missing measurements. The switched system under study involves stochastic disturbance, time‐varying discrete delay, bounded distributed delay and nonlinearity. Attention is focused on the design of a mode‐dependent filter that guarantees the exponential stability in the mean‐square sense and a prescribed H_∞ noise attenuation level for the filtering error dynamics. By constructing a new Lyapunov functional and using the average dwell time scheme, a new delay‐dependent sufficient condition for the existence of the filter is presented in terms of linear matrix inequalities. A numerical example is finally given to show the effectiveness of the proposed design method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Delay‐range‐dependent H∞ control for Markovian jump systems with mode‐dependent time delays

This paper considers mean‐square exponential stability and H_∞ control problems for Markovian jump systems (MJSs) with time delays which are time‐varying in an interval and depend on system mode. By exploiting a novel Lyapunov‐Krasovskii functional which takes into account the range of delay, and by making use of some techniques, new delay‐range‐dependent stability result and bounded real lemma for MJSs are obtained, where the introduction of the lower bound of delay is shown to be advantageous for reducing conservatism. Moreover, a sufficient condition for the solvability of the H_∞ control problem is derived in terms of linear matrix inequalities. Finally, illustrative examples are presented to show the advantage and effectiveness of the proposed approaches. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Improved stability and H∞ performance criteria for linear systems with interval time-varying delays via three terms approximation

This paper investigates the problem of delay dependent stability and H_∞ performance for a class of linear systems with interval time-varying delay. A new model transformation is first proposed by employing a three-terms approximation of delayed state variables, for a better approximation of delayed state. By using scaled small gain theorem and a simple Lyapunov–Krasovskii functional, new stability and H_∞ performance criteria are proposed in terms of linear matrix inequalities, which can be easily solved by using standard numerical packages. Finally, numerical examples are presented to illustrate the effectiveness of the proposed method.     

An improved characterization of bounded realness for singular delay systems and its applications

This paper is concerned with establishing a delay‐dependent bounded real lemma (BRL) for singular systems with a time delay. Without resorting to any bounding techniques for some cross terms and model transformation, a new version of BRL for such systems is proposed, which guarantees a singular system to be regular, impulse free and stable while satisfying a prescribed H_∞ performance level for any delays smaller than a given upper bound. Based on this, an H_∞ state feedback controller is designed via a linear matrix inequality approach. The BRL, stability as well as H_∞ results developed in this paper are less conservative than existing ones in the literature, which is demonstrated by providing some numerical examples. Copyright © 2007 John Wiley & Sons, Ltd.     

具有扇区有界非线性时变时延离散系统的非脆弱H_infinity控制

研究具有扇区有界非线性时变时延离散系统的非脆弱非线性记忆状态反馈H∞控制器的设计问题.提出一种具有更一般性的控制器增益不确定,并采用Lyapunov-Krasovskii泛函及线性矩阵不等式技术给出了控制器设计的一个时滞依赖的充分条件.最后通过一个例子验证了所提出方法的有效性.     

A new delay system approach to network-based control

This paper presents a new delay system approach to network-based control. This approach is based on a new time-delay model proposed recently, which contains multiple successive delay components in the state. Firstly, new results on stability and H_∞ performance are proposed for systems with two successive delay components, by exploiting a new Lyapunov-Krasovskii functional and by making use of novel techniques for time-delay systems. An illustrative example is provided to show the advantage of these results. The second part of this paper utilizes the new model to investigate the problem of network-based control, which has emerged as a topic of significant interest in the control community. A sampled-data networked control system with simultaneous consideration of network induced delays, data packet dropouts and measurement quantization is modeled as a nonlinear time-delay system with two successive delay components in the state and, the problem of network-based H_∞ control is solved accordingly. Illustrative examples are provided to show the advantage and applicability of the developed results for network-based controller design.     

Robust stability of nonlinear time‐delay systems with interval time‐varying delay

This paper deals with the problem of obtaining delay‐dependent stability conditions and L₂‐gain analysis for a class of nonlinear time‐delay systems with norm‐bounded and possibly time‐varying uncertainties. No restrictions on the derivative of the time‐varying delay are imposed, though lower and upper bounds of the delay interval are assumed to be known. A Lyapunov–Krasovskii functional approach is proposed to derive novel delay‐dependent stability conditions which are expressed in terms of linear matrix inequalities (LMIs). To reduce conservatism, the work exploits the idea of splitting the delay interval in multiple regions, so that specific conditions can be imposed to a unique functional in the different regions. This improves the computed bounds for certain delay‐dependent integral terms, providing less conservative LMI conditions. Examples are provided to demonstrate the reduced conservatism with respect to the available results in the literature. Copyright © 2010 John Wiley & Sons, Ltd.