一类非线性组合大系统的稳定性

本文研究一类比较广泛的非线性组合大系统的稳定性问题.基于矩阵代数Riccati 方程存在对称正定解的新判据(引理2),给出了检验这类非线性组合大系统稳定性的新准 则,所给出的稳定性准则只涉及子系统的稳定性以及子系统之间的互联项,因此,当应用该准 则检验这类非线性组合大系统的稳定性时,避免了构造子系统以及大系统的Lyapunov函数 的困难.     

一类具有对称内联子系统的不确定大系统的二次稳定性

本文研究了一类由若干个相似子系统和一个外部系统通过对称地内联组成的不确定大系统的二次稳定性问题用二个低阶子系统以及相应的Ｈ∞范数的术语给出了这样一个系统是二次稳定的充分条件，并且证明了这个条件对于这个系统的过界系统的二次稳定性也是必要的。     

不确定线性组合大系统的二次稳定性、联结稳定性与H∞小增益定理

本文首先讨论了不确定线性系统(t)={A+DiFi(t)E}x(t)的二次稳定性,得到了该系统是二次稳定的充分必要条件.基于本文得到的结论讨论了不确定线性组合大系统的二次稳定性和联结稳定问题,得到了用关于低阶子系统的一组H∞模描述大系统稳定性的充分条件.     

不确定线性组合大系统的二次稳定性、 联结稳定性H∞小增益定理

本文首先讨论了不确定线性系统ｘ＾．（ｔ）＝｛Ａ＋＾ｋΣｉ＝１ＤｉＦｉ（ｔ）Ｅ｝ｘ（ｔ）的二次稳定性,得到了该系统是二次稳定的充分必要条件。基于本文得到的结论讨论了不确定线性组合大系统的二次稳定性和联结稳定问题,得到了用关于低阶子系统的一组Ｈ∞模描述了大系统稳定性的充分条件。     

具有无穷时滞的不确定大系统的鲁棒镇定

研究了具有无穷时滞的不确定微分－积分大系统的鲁棒稳定性问题，对每个子系统的应用稳定的局部状态反馈，利用Lyapunov函数法并结合不等式分析技巧，给出了具有无穷时滞的不确定微分－积分大系统的鲁棒全局一致近稳定的充分条件。     

一类广义相似组合系统的鲁棒渐近观测器设计

描述两个控制系统间的广义相似性概念,并针对一类具有不确定参数的非线性广义相似大系统设计出一种具有相似结构的鲁棒渐近状态观测器。这类组合系统可由若干个不同状态维数的子系统构成。算例结果表明了所采用方法的有效性。     

一类非线性组合大系统的分散输出反馈鲁棒镇定1)

研究了不确定非线性子系统经不确定非线性互联而成的组合大系统,给出了其可分散输出反馈鲁棒镇定的充分条件,说明了所得结论的广泛适用性以及相似结构与全息特性的密切相关性.     

一类非线性组合大系统的分散输出反馈鲁棒镇定

研究了不确定非线性子系统经不确定非线性互联而成的组合大系统,给出了其可分 散输出反馈鲁棒镇定的充分条件,说明了所得结论的广泛适用性以及相似结构与全息特性的 密切相关性.     

基于切换原理的非均匀采样系统控制

在非均匀采样系统中,存在着刷新时间间隔不确定、时变的情况,这给系统控制器的设计造成了很大困难.为此,将刷新时间间隔看作时延变量,不同时延大小情况下的系统动态变化用不同子系统模型刻画,从而将时延的变化律转化为不同子模型之间的切换律,将非均匀采样系统描述为一类具有有限个子系统的离散时间切换系统.通过定理形式给出含有不确定刷新时间间隔的反馈闭环系统鲁棒稳定性的充分条件.     

广义对称组合系统的结构分析

研究了由若干个相同的广义线性子系统以对称的内联方式构成的广义对称组合大系统的性质.首先,通过系统变换,将原广义对称组合大系统转换为两个低阶的修正子系统,然后通过分析得到广义对称组合大系统的稳定性、能控性、能观性、固定模的存在性、分散正常化、Lyapunov方程和Riccati方程的解等性质,均可由这两个低阶的修正子系统的相应性质来描述.     

DECENTRALIZED ROBUST CONTROL DESIGN FOR A CLASS OF SIMILAR COMPOSITE SYSTEMS WITH UNCERTAINTIES

A class of similar composite systems is researched. The interconnections of systems are not symmetric and do not satisfy the matching condition. By means of the advantage of interconnections of systems, a two-step method is proposed to study the decentralized stabilization problem for the similar composite systems in this paper. First, the interconnections between subsystems are changed into a new form to satisfy the matching condition; second, based on the new form of the systems, the decentralized robust controllers are designed. In this paper, the controllers guarantee the similar composite systems quadratic stability. At last, the simulation of example is given.     

不确定非线性环链系统的分散鲁棒控制

提出了环链系统和一类不确定非线性环链系统,利用线性代数理论,给出了实现环链系统的充要条件,运用李雅普诺夫稳定理论和矩阵理论研究了不确定非线性环链系统的鲁棒镇定,并给出了一种非线性鲁棒镇定控制器的设计,还考虑了一类非线性环链相似组合大系统,给出了分散鲁棒镇定条件,最后给出数值例子说明设计方法的有效性。     

一类不确定离散切换模糊组合系统的稳定性控制

以模糊T-S模型对离散切换组合系统的研究模型进行重新构建,分别利用单Lyapunov函数方法设计出分散切换律和控制器,给出了利用矩阵不等式表达的系统在分散切换律和分散控制器作用下的可镇定条件,仿真结果表明了该方法的有效性。     

Modeling and stability analysis of hybrid dynamical systems based on extended differential Petri nets

In this paper, extended differential Petri nets (EDPNs), a new extension of differential Petri nets (DPNs), is proposed. Compared with the existing extension of DPNs, EDPNs has two improvements: (1) the restriction on the enabling condition that depends on the weight of arc is relaxed, i.e., allow the enabling condition has more general form; (2) the definition is extended for the weight of arc. By these two improvements, EDPNs presents larger flexibility and modeling power than the existing extension of DPNs. Using this model, the stability of hybrid dynamical systems (HDS) is studied. A new Lyapunov’s stability theorem of HDS is given. Furthermore, by using the information of index matrix and a new composite energy function, the stability theorem of linear HDS is obtained.     

Local stability of composite systems--Frequency-domain condition and estimate of the domain of attraction

This paper is concerned with such composite systems whose subsystems contain one nonlinearity each and whose interconnections are functions of the scalar outputs of subsystems. A frequency-domain condition which assures local asymptotic stability is given under the assumptions that each nonlinearity satisfies a sector condition, that interconnections are linearly bounded, and that linear parts of subsystems may have unstable poles. In deriving the above result, such Lyapunov functions of subsystems are constructed so that their weighted sum is a Lyapunov function of the overall system. A method to estimate the domain Of attraction based on the above Lyapunov functions is also studied. When the bounds on nonlinearities hold true in the entire space and when the linear parts do not have unstable poles, the present condition turns out to be the same with the L2-stability condition which was obtained before by Araki.     

具有时滞的Lurie型组合系统的分散输出反馈镇定

通过构造一比较系统,将Lurie型组合系统的稳定性问题转化为讨论维数较低的比较系统的稳定性问题,并利用M矩阵特性导出比较系统稳定的一个充分条件;为求取输出反馈增益,建立等价的稳定条件的QLMI表示形式.这一方法的特点是使大系统的稳定控制器设计的复杂度保持在子系统一级的水平上,给出的实例说明算法在实际工程应用中是有效的.     

The Controllability,Observability, and Stability Analysis of a Class of Composite Systems with Fractional Degree Generalized Frequency Variables

This paper is concerned with fundamental properties of a class of composite systems with fractional degree generalized frequency variables, including controllability, observability and stability. Firstly, some necessary and sufficient conditions are given to guarantee controllability and observability of such composite systems. Then we prove that the stability problem of such composite systems can be reduced to judging whether a fractional degree polynomial is stable. Finally, the stability analysis result is applied in the supervisory control of fractional-order multi-agent systems, and an example is provided to illustrate the effectiveness of the proposed methods.      

基于状态观测器的非理想输入不确定组合大系统的输出反馈分散镇定

基于状态观测器,讨论了不确定相似组合系统的鲁棒分散输出反馈镇定问题,系统的输入是非理想的,不确定项存在于系统内部和各子系统的关联项中,它们可能是非线性或时变的,且满足通常的匹配条件,使用变结构原理设计控制器,所设计的控制器保证系统渐近稳定,研究结果表明,系统的相似性有助于简化对系统的分析和设计;仿真结果表明,本文的方法是有效的。     

Dynamic stability analysis of a composite material planar mechanism by the finite element method

Vibration analysis has become one of the most important considerations in the design of machines for high-speed operation. Dynamic stability may occur in high-speed flexible mechanisms. The use of composite materials which possess high strength to weight and high stiffness to weight ratios may improve these problems. The Euler beam theory is used to study the dynamic stability of a planar four-bar mechanism made from composite material. The operation condition is assumed to be at a steady dynamic state. The Ritz finite element procedure is used to solve the dynamic stability problem. The advantages of using composite materials are demonstrated.