不确定时滞系统鲁棒镇定新方法

针对一类同时具有状态和控制滞后的不确定时滞系统,提出了一种新的时滞依赖型鲁棒镇定设计方法.通过引入一种新的线性状态变换,分离出时滞依赖因子,采用Lyapunov-Krasovskii泛函方法,导出了不确定时滞系统可鲁棒镇定的时滞依赖型的新判据,所得结论以线性矩阵不等式组的解的形式表示.仿真结果表明所得结论较之已有结果更为简单,具有更小保守性,且有更广泛的应用范围,不仅可以解决小时滞问题,也可用于解决大时滞问题.     

一类线性离散时滞大系统的分散镇定

用一组线性矩阵不等式给出一类线性离散时滞大系统分散能镇定的一个充分条件,进而,通过建立和求解一个凸优化问题,提出了具有较反馈增益参数的分散稳定化状态反馈控制律的设计方法,所得到的控制器不仅使得闭环境系统是稳定的,而且还可以使得闭环系统状态具有给定的衰减度。     

含未知输入的时滞系统的函数观测器及输出反馈镇定

考虑了含未知输入的时滞系统的线性函数观测器设计.在一个不失一般性的秩条件假定下,以线性矩阵不等式(LMI)的形式给出了观测器存在的时滞无关型及时滞相关型判据,进而得到函数观测器改进的设计方法.此外,还讨论了降维状态观测器的设计,给出了基于观测器的反馈镇定控制器,实现了闭环的特征根分离及内稳定.具体算例说明了本文方法的有效性.     

一类线性时滞系统的鲁棒稳定性分析

针对一类具有范数有界不确定性和2个继发时变时滞的线性时滞不确定系统,研究了其时滞依赖鲁棒稳定性问题.通过定义充分利用时变时滞上下界信息的新型Lyapunov-Krasovskii泛函,并结合时滞系统相关处理方法和线性矩阵不等式方法,得到了时滞线性不确定系统鲁棒渐近稳定所满足的条件.为了降低结论的保守性,对某些项进行了较紧致的估计.此外,并未引入自由权矩阵.最后并通过2个数值仿真证实了方法的有效性和优越性.     

不确定广义系统的时滞依赖鲁棒镇定

研究不确定广义系统的时滞依赖鲁棒镇定问题。利用Lyapunov泛函方法,得到一个线性矩阵不等式(LMIs)形式的时滞依赖稳定与镇定判据。新方法考虑一些以前方法中通常忽略的有用的项,引入一些自由权重矩阵,估计Lyapunov泛函导数的上界;再用凸优化算法,进一步给出状态反馈控制器的设计方法。最后通过两个仿真示例表明了新方法的有效性。     

一类区间时变时滞T-S模糊系统的鲁棒控制

针对一类区同时变时滞T-S模糊系统,研究了其时滞相关渐近稳定性以及控制器设计问题.基于Lyapunov稳定性理论和线性矩阵不等式(LMI)工具,并结合自由权矩阵方法,设计一个包含时滞区间均值在内的新Lyapunov-Krasovskii泛函,给出了改进的时滞T-S模糊系统渐近稳定的时滞相关准则.同时,根据并行分布补偿算法,给出了带有记忆的状态反馈模糊控制器的设计方法.最后,实例仿真表明了方法的有效性.     

线性时滞系统的输入-输出能量解耦

提出一种针对具有时变时滞的线性时滞系统的能量解耦方法,即从输入-输出的能量关系上实现解耦,使得任何一个输入的能量主要控制对应的一个输出的能量,对其它输出能量的影响尽可能小.该解耦方法兼有静态解耦与动态解耦的特点.所有结论均由线性矩阵不等式描述.     

线性不确定时滞系统指定衰减度鲁棒镇定

研究了一类线性不确定时滞系统时滞依赖型具有指定衰减度的无记忆状态反馈鲁棒镇定问题.所考虑的线性不确定时滞系统含有时变未知但有界的不确定参数和状态滞后.通过应用Razumikhin定理和Lyapunov定理,导出了系统鲁棒稳定且具有指定衰减度的判据和具有指定衰减度的无记忆状态反馈鲁棒镇定控制律存在的充分条件及相应的控制器设计方法.所得时滞相关的结果用一组线性矩阵不等式(LMI)表示.     

线性离散时滞系统的输出反馈耗散控制

考虑线性离散时滞系统的二次型耗散控制问题,设计动态输出反馈使闭环系统渐近稳定且严格二次型耗散.先将系统严格二次型耗散性转化为线性矩阵不等式的可解性,得到了系统渐近稳定且严格二次型耗散的条件.然后讨论输出反馈耗散控制问题,给出了控制器的存在条件,总结出了控制器的综合方法、步骤.所得结果可为离散时滞系统的无源控制和H∞控制提供统一框架,也为离散时滞系统的分析和设计提供了一种更灵活、保守性更小的方法.     

改进的时变时滞不确定离散系统的鲁棒稳定性分析

研究了一类具有区间时变时滞的不确定离散时间系统的鲁棒稳定性问题.首先,将时滞区间分成两个子区间,在不同的子区间上通过构造不同的Lyapunov泛函,再结合一个更紧的不等式,在没有忽略任何有用项的前提下,得到了基于线性矩阵不等式形式的时滞相关的稳定性判据.证明过程既没有利用模型变换也没有引进自由权矩阵,降低了结论的保守性和计算量.数值算例说明了该方法的有效性.     

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.     

时滞广义区间系统的弹性保性能控制

研究了一类时滞广义区间系统的弹性保性能控制问题.利用线性矩阵不等式处理方法,导出了系统弹性保性能控制器存在的条件,证明了该条件等价于一个线性矩阵不等式的可行性问题,并用该线性矩阵不等式的可行解给出了弹性保性能控制器的一个参数化表示.进一步,通过求解一个凸优化问题,给出了系统的最优弹性保性能控制器的设计方法.最后的数值例子说明了所给方法的有效性.     

Delay-dependent observer-based stabilizing controller design for linear multiple state-delayed systems

This article concerns a coupled LMIs approach to delay-dependent observer-based output feedback stabilizing controller design for linear continuous-time systems with multiple state delays. The advantage of our proposed delay-dependent coupled LMIs criterion lies in that: (1) it can optimize one of multiple time delays with others selected properly, and at the same time, the feedback-gain and observer-gain can be obtained, respectively. (2) it is less conservative than the existing delay-independent ones in the literature. Algorithm to solve the coupled LMIs is also given. Numerical examples illustrate the effectiveness of our method.     

线性时滞广义系统的时滞相关H∞控制

讨论线性时滞广义系统的时滞相关H∞控制.首先利用Park不等式建立了一个基于二次型项的积分不等式,然后利用Lyapunov_Krasovskii泛函方法,获得了系统经慢子系统的无记忆状态反馈后不仅内部稳定,而且具有给定的H∞性能的,基于LMI的时滞相关充分条件.数值例子表明本文方法所得结论较已有文献具有较小的保守性.     

基于鲁棒可靠性的不确定时滞系统最优H∞控制器设计

用区间变量描述控制系统参数的不确定性,提出了不确定时滞系统鲁棒H_∞控制的鲁棒可靠性方法,基于鲁棒可靠性的不确定时滞系统最优状态反馈H_∞控制器设计方法,将系统的最优控制器设计归结为基于线性矩阵不等式(LMI)的优化问题．所设计的控制器可以在满足对所有不确定性鲁棒可靠的前提条件下,具有最优的H_∞鲁棒性能,并能在控制系统的设计中综合考虑控制性能、控制代价和鲁棒可靠性．数值算例说明了所提方法的有效性和可行性．     

离散广义区间系统的保成本控制

分析了离散广义区间系统的保成本控制问题.当系统参数在某一确定区间变化时,控制器能保证闭环系统稳定和一定的线性二次型性能指标上界.基于Lyapunov稳定性理论,该控制器的设计可转化为线性矩阵不等式的可解性问题.数值仿真也验证了所给方法的有效性.     

LMI-based robust iterative learning controller design for discrete linear uncertain systems

This paper addresses the design problem of robust iterative learning controllers for a class of linear discrete-time systems with norm-bounded parameter uncertainties. An iterative learning algorithm with current cycle feedback is proposed to achieve both robust convergence and robust stability. The synthesis problem of the proposed iterative learmng control （ILC） system is reformulated as a γ-suboptimal H-infinity control problem via the linear fractional transformation （LFT）. A sufficient condition for the convergence of the ILC algorithm is presented in terms of linear matrix inequalities （LMIs）. Furthermore, the linear wansfer operators of the ILC algorithm with high convergence speed are obtained by using existing convex optimization techniques. The simulation results demonstrate the effectiveness of the proposed method.     

Delay-range-dependent stability criterion for interval time-delay systems with nonlinear perturbations

In this paper, we consider the problem of robust stability for a class of linear systems with interval time-varying delay under nonlinear perturbations using Lyapunov-Krasovskii (LK) functional approach. By partitioning the delay-interval into two segments of equal length, and evaluating the time-derivative of a candidate LK functional in each segment of the delay-interval, a less conservative delay-dependent stability criterion is developed to compute the maximum allowable bound for the delay-range within which the system under consideration remains asymptotically stable. In addition to the delay-bi-segmentation analysis procedure, the reduction in conservatism of the proposed delay-dependent stability criterion over recently reported results is also attributed to the fact that the time-derivative of the LK functional is bounded tightly using a newly proposed bounding condition without neglecting any useful terms in the delay-dependent stability analysis. The analysis, subsequently, yields a stable condition in convex linear matrix inequality (LMI) framework that can be solved non-conservatively at boundary conditions using standard numerical packages. Furthermore, as the number of decision variables involved in the proposed stability criterion is less, the criterion is computationally more effective. The effectiveness of the proposed stability criterion is validated through some standard numerical examples.     

Observer‐based controller design of discrete‐time piecewise affine systems

This paper presents a novel observer‐based controller design method for discrete‐time piecewise affine (PWA) systems. The basic idea is as follows: at first, a piecewise linear (without affine terms) state feedback controller and a PWA observer are designed separately, and then it is proved that the output feedback controller constructed by the resulting observer and state feedback controller gains can guarantee the stability of the closed‐loop system. During the controller design, the piecewise‐quadratic Lyapunov function technique is used. Moreover, the region information is taken into account to treat the affine terms, so the controller gains can be obtained by solving a set of linear matrix inequalities, which are numerically feasible with commercially available software. Three simulation examples are given finally to verify the proposed theoretical results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society