不确定时滞分布参数系统鲁棒控制的LMI方法

对常时滞、变时滞的不确定分布参数控制系统,提出了一种与现有的研究分布参数控制系统不同的鲁棒控制方法.该方法通过构造平均Lyapunov函数,利用线性矩阵不等式知识,在只要求系统本身所固有的系数是负定矩阵的条件下,给出了所给的分布参数系统镇定的充分条件.当模型中的时滞为常时滞时,所得的充分条件与时滞无关.当模型中的时滞为变时滞时,所得模型的镇定准则依赖于时滞.此外,该方法与已有方法比较的一个显著优点就是所获得的条件容易检验,因而易于应用.最后举了一个实例以说明该方法的有效性.     

一类具有连续分布时滞的分布参数系统的反馈控制

针对一类同时具有变时滞和连续分布时滞的分布参数系统的状态反馈控制问题进行了研究,通过选择适当的Lyapunov-Krasovskii函数,采用线性矩阵不等式(LMI)方法,得到了变时滞闭环系统渐近稳定的一个充分条件.设计了无记忆的状态反馈控制器,使得在一个正定矩阵存在的条件下,闭环系统是可镇定的,从而得到了常时滞分布参数系统可镇定的一个推论.最后,通过一个数值仿真例子说明了所给出设计方法的可行性和有效性.     

具有多个时滞的积分时滞系统的稳定性分析

首先,针对具有多个时滞的积分时滞系统,建立新的基于线性矩阵不等式的稳定性条件.该条件与正整数k有关,给出$k=1$时该条件与现有结果间的关系.该关系表明所提出条件在$k\geqslant2$时的保守性比现有结果小;然后,基于所提出的稳定性条件,进一步研究具有参数不确定性的积分时滞系统的鲁棒稳定性问题,建立基于线性矩阵不等式的充分条件;最后,利用所提出方法,研究具有多个离散时滞和分布时滞的积分时滞系统的稳定性问题.数值算例结果表明了所提出稳定性判据的有效性.     

多组时滞大型控制系统的镇定

给出了由无时滞线性定常闭孤立控制子系统的渐近稳定性推出多组时滞线性定常闭环大型控制系统的渐近稳定性的充分条件，并说明了所得结果可以推广到多组时滞线性时变闭环大型控制系统与多组时滞线中立型定常（或时变）闭环大型控制系统，所得结果改进了前人的结果，通过参数镇定域的比较知，可使参数镇定域扩大为原来的６倍。     

一类含未建模动态的奇异时滞系统的鲁棒镇定问题

利用线性矩阵不等式的方法，研究了一类同时含有参数摄动和未建模动态的线性奇异时滞系统的鲁棒镇定问题.得到了系统可鲁棒镇定的一个充分条件，用线性矩阵不等式的方法，将控制器的求解问题转化为受限线性矩阵不等式的求解问题，并给出了受限线性矩阵不等式的具体解法．最后举例说明了所提出方法的正确性．     

时变时滞不确定系统的鲁棒输出反馈控制

研究了时变时滞不确定系统基于状态观测器的动态输出反馈实现鲁棒镇定的分 析和综合问题.所研究的系统不仅同时包含时变状态时滞和时变控制时滞,而且包含时变未 知且有界不确定参数.提出了确保该系统可通过输出反馈鲁棒镇定的充分条件,并将该充分 条件转化为线性矩阵不等式(LMI)问题,最终通过求解两个LMI来构造输出反馈控制律.     

变时滞分布参数系统的全局指数稳定性

基于比较原理,利用推广的向量Hanalay微分不等式,Dini导数,结合Green公式及不等式分析技术,研究几类变时滞分布参数控制系统所导出的滑动模运动方程的全局指数稳定性问题,在仅要求系数矩阵是个M-矩阵的条件下,获得了几类滑动模运动方程全局指数稳定性的充分条件,建立了滑动模运动方程全局指数稳定性定理.推广和改进了前人的结论.并为研究时滞分布参数系统的变结构控制问题奠定了基础.     

多模式网络化控制系统稳定性分析

网络传输引起的时滞在网络化控制系统中经常出现．针对存在多个运动模式的网络化控制系统,建立了时滞混杂自动机模型,分析了系统平衡点的稳定性,给出了平衡点保持稳定的充分条件在于构造的与离散状态相关的Lyapunov泛函在离散状态的切换时刻是非增的．当时滞混杂自动机中连续性子系统为线性时不变时滞系统时,可以利用线性矩阵不等式方法来寻找系统的公共Lyapunov泛函,并求解使系统平衡点保持稳定的时滞上界．最后,给出了一个例子说明了分析结果．     

线性时滞关联大系统的分散α-镇定

通过分析线性时滞关联大系统超越型的特征议程的根的分布,并结合线性矩阵不等式(LMI)技术研究了含多个不确定常时滞的线性时滞关联大系统的可分散α-镇定问题,得到了相应的分散α-反馈控制律．不同于一般的结果,本方法得到的分散控制器不但使得系统可分散镇定,而且还可以确定闭环系统特征方程的根的实部的上界．结果表示为LMI形式,易于进行数值处理．最后以一个数值例子显示了所得结果的有效性及其应用方法．     

不确定性关联奇异大系统时滞相关分散鲁棒镇定

针对一类不确定关联时滞奇异大系统,利用Lyapunov稳定性理论与时滞积分矩阵不等式相结合的方法,研究其时滞相关分散鲁棒镇定问题,目的是设计一无记忆状态反馈分散控制器,使闭环系统鲁棒稳定.用矩阵不等式方法,给出了该类系统时滞相关分散鲁棒镇定的充分条件.所得结果与系统时滞的大小有关,并以矩阵不等式的形式给出.最后用数值算例说明了所给方法的可行性和有效性.     

Stabilization of linear systems with distributed input delay and input saturation

This paper is concerned with stabilization of a linear system with distributed input delay and input saturation. Both constant and time-varying delays are considered. In the case that the input delay is constant, under the stabilizability assumption on an auxiliary system, it is shown that the system can be stabilized by state feedback for an arbitrarily large delay as long as the open-loop system is not exponentially unstable. In the case that the input delay is time-varying, but bounded, it is shown that the system can be stabilized by state feedback if the non-asymptotically stable poles of the open-loop system are all located at the origin. In both cases, stabilizing controllers are explicitly constructed by utilizing the parametric Lyapunov equation based low gain design approach we recently developed. It is also shown that in the presence of actuator saturation and under the same assumptions on the system, these controllers achieve semi-global stabilization. Some discussions on the assumptions we impose on the system are given. A numerical example illustrates the effectiveness of the proposed stabilization approach.     

Delay-independent stability criteria for linear continuous systems with time-varying delays

New stability criteria for linear continuous systems with multiple time-varying delays are established by the Lyapunov function approach based on a new stability theorem for general type of retarded dynamical systems. A new technique for estimating the derivative of Lyapunov function along the solution of system at some specific instants is used so that the case of multiple time-varying delays can be dealt with less conservatively. In addition, (i) every criterion has only one tuning parameter matrix P>0 as the Lyapunov-type stability criterion for the corresponding linear continuous system without delays does; (ii) all the criteria are given in LMI forms and hence they are numerically tractable. It is remarked that the established criteria are less conservative than the existing ones in the literature. Three examples are given to illustrate the proposed method and to show the superiority of the obtained results to the existing ones in the literature.     

Decentralized stabilization of large-scale linear continuous systems with N X N time-varying delays

In this paper, a decentralized stabilization condition for large-scale linear continuous systems with N x N time-varying delays is established under a decomposition case of the interconnections. Based on a new stability theorem for a general type of retarded dynamic systems, the results are derived by using the Lyapunov function instead of the L yapunov functional. During the derivation, a new technique for estimating the derivative of the L yapunov function for the solution of the system under consideration is used so that the case of N x N time-varying delays can be dealt with as least conservatively as possible. It is noted that the stabilization condition obtained by using the proposed technique is better than those obtained by using the existing Razumikhin-type techniques in the literature. An example with three interconnected subsystems is given to illustrate the proposed method and to show the design of the local memoryless state feedback controllers.     

Global exponential stability analysis of cellular neural networks with multiple time delays

Global exponential stability problems are investigated for cellular neural networks (CNN) with multiple time-varying delays. Several new criteria in linear matrix inequality form or in algebraic form are presented to ascertain the uniqueness and global exponential stability of the equilibrium point for CNN with multiple time-varying delays and with constant time delays. The proposed method has the advantage of considering the difference of neuronal excitatory and inhibitory effects, which is also computationally efficient as it can be solved numerically using the recently developed interior-point algorithm or be checked using simple algebraic calculation. In addition, the proposed results generalize and improve upon some previous works. Two numerical examples are used to show the effectiveness of the obtained results.     

Global exponential stability analysis of cellular neural networks with multiple time delays

Global exponential stability problems are investigated for cellular neural networks （CNN） with multiple time-varying delays. Several new criteria in linear matrix inequality form or in algebraic form are presented to ascertain the uniqueness and global exponential stability of the equilibrium point for CNN with multiple time-varying delays and with constant time delays. The proposed method has the advantage of considering the difference of neuronal excitatory and inhibitory effects, which is also computationally efficient as it can be solved numerically using the recently developed interior-point algorithm or be checked using simple algebraic calculation. In addition, the proposed results generalize and improve upon some previous works. Two numerical examples are used to show the effectiveness of the obtained results.     

Delay-dependent robust stabilization of uncertain systems withmultiple state delays

This paper deals with the problem of robust stabilization for uncertain systems with multiple state delays. The parameter uncertainties are time-varying and unknown but are norm-bounded, and the delays are time-varying. A new method for achieving robust stabilization is presented for a class of uncertain time-delay systems via linear memoryless state feedback control. The results depend on the size of the delays and are given in terms of several linear matrix inequalities     

Delay-range-dependent robust stabilization for uncertain T-S fuzzy control systems with interval time-varying delays

This paper is concerned with robust stabilization for a class of T-S fuzzy control systems with interval time-varying delays. An approach is proposed to significantly improve the system performance while reducing the number of scalar decision variables in linear matrix inequalities. The main points of the approach are: (i) two coupling integral inequalities are proposed to deal with some integral items in the derivation of the stability criteria; (ii) an appropriate Lyapunov-Krasovskii functional is constructed by including both the lower and upper bounds of the interval time-varying delays; and (iii) neither model transformation nor free weighting matrices are employed in the theoretical result derivation. As a result, some improved sufficient stability criteria are derived, and the maximum allowable delay bound and controller gains can be obtained simultaneously by solving an optimization problem. Numerical examples are given to demonstrate the effectiveness of the proposed approach.     

Exponential stability of genetic regulatory networks with mixed delays by periodically intermittent control

This paper investigates the exponential stability for a class of mixed delayed genetic regulatory networks by periodically intermittent control, mixed delays here include time-varying delays and finite distributed delays. Some sufficient criteria for exponential stabilization are derived by using mathematical induction methods and the analysis techniques. Finally, an example is presented to demonstrate the effectiveness of the theoretical results.     

Nonfragile Hinfinity control for uncertain neutral systems with time-varying delays via the LMI optimization approach.

The nonfragile Hinfinity control problem for a neutral system with time-varying delays is considered. Delay-dependent criteria are proposed to guarantee the stabilization and disturbance attenuation of systems. A linear matrix inequality optimization approach is used to solve the nonfragile Hinfinity control problem. Nonfragile Hinfinity control for an unperturbed neutral system is investigated first. Then, nonfragile Hinfinity control for an uncertain neutral system is derived directly from the unperturbed case. Finally, two examples are illustrated to show the improvement of this correspondence.     

具有多时变时滞的单一和复合线性系统的时滞无关稳定性判据

针对单一和复合多时变时滞系统分别建立了稳定性的充分条件,结果的推导采用了拉什密辛（Ｒａｚｕ－ｍｉｋｈｉｎ）定理结合代数不等式的方法,同时,本文提出了一些优化稳定性判据中参数的方法,所建判据既不依赖于时滞的大小也不依赖时滞的导数,故既适用于时变时滞系统也适用于常时滞系统或无无时滞系统,最后,给出了一些例子所提方法的应用,并比较文献中存在的结果。