参数不确定性广义周期时变系统的鲁棒稳定性分析

基于广义周期时变系统允许的充分必要条件,提出了参数不确定性广义周期时交系统鲁棒稳定的概念,并得到了该类系统鲁棒稳定的充分必要条件．研究在状态反馈控制下保证闭环系统鲁棒稳定的条件,给出了一族状态反馈鲁棒稳定器的设计方法．引入广义周期时变系统二次稳定的概念,讨论了二次稳定性与鲁棒稳定性的关系．最后通过数值算例说明了所得的主要结果,     

具有结构不确定性的线性反馈控制系统的鲁棒稳定性

本文研究了具有结构不确定性(Structured Uncertainty)因素的反馈控制系统的鲁棒稳定性问题,对于一个普通的补偿器,给出了闭环系统鲁棒稳定的充要条件,当补偿器满足某些假设条件时,得出了闭环系统鲁棒稳定的有限检验的充分必要条件.     

参数不确定时滞系统的鲁棒稳定性

研究一类具有参数不确定时滞系统的鲁棒稳定性问题．假定其线性部分的参数不确定性由区间摄动模武描述,非线性部分的动态不确定性由积分二次约束(IQC)描述,给出了时滞互联系统鲁棒稳定的充分条件,并根据IQC乘子的特性,将无穷维稳定性检验问题转化为一维检验或有限检验问题．     

具有结构不确定性的输出反馈性系统的鲁棒稳定性分析

基于向量的幂变换方法，对具有结构不确定性的输出反馈线性系统的鲁棒稳定性问题作了分析。单参数摄动时给出了闭环系统鲁棒稳定的充要条件，多参数摄动时得到了保证系统鲁棒稳定的充分条件，导出了闭环系统鲁棒稳定区域的一种代数表达形式。最后给出了实例。     

具有线性和非线性结构式不确定性的多变量系统的鲁棒稳定性

本文研究具有多重扇形非线性环节和结构式线性不确定性系统的鲁棒稳定性。给出了检验含参数不确定性和未建模动态的多变量Ｌｕｒｉｅ系统鲁棒绝对稳定的统一判据,并证明了多变量Ｐｏｐｏｖ判据和混合μ上界均是该判据的特殊形式。基于Ｒｏｓｅｎｂｒｏｃｋ优于算法和内点法,本文还给出了计算这一判据的一种凸优化算法。最后用一计算示例表明本文结果还可用于确定含参数不确定性和未建模动态的Ｌｕｒｉｅ系统的Ｈ∞性能。     

不确定性系统族的鲁棒稳定裕度

本文给出了不确定性系统族的鲁棒稳定裕度定义以及计算方法。这些结果具有非常一般化的意义。     

不确定广义双线性系统的鲁棒镇定

针对带有不确定参数的广义双线性系统的鲁棒镇定问题进行研究, 其中不确定参数是时变且范数有界的. 本文的目的是设计状态反馈控制器, 使得对所有满足条件的不确定参数闭环系统都是渐近稳定的. 通过引入广义二次稳定的概念、采用Lyapunov方法, 分别给出了不确定广义双线性系统在两种不同情形下可镇定的充分条件; 此外, 两个数值例子分别说明了两种设计方法的有效性和合理性.     

混合不确定系统的鲁棒稳定性

研究兼有参数不确定性和非结构不确定性的混合不确定系统的鲁棒稳定性,该问题可以转化为具有参数摄动的传递函数族的最大H∞范数的计算问题,针对区间对象的加权H∞范数的最大值问题,给出了精确的计算公式并讨论了顶点检验成立的条件.     

具有结构不确定性的输出反馈线性系统的鲁棒稳定性分析

基于向量的幂变换方法，对具有结构不确定性的输出反馈线性系统的鲁棒稳定性问题作了分析。单参数摄动时给出了闭环系统鲁棒稳定的充要条件，多参数摄动时得到了保证系统鲁棒稳定的充分条件，导出了闭环系统鲁棒稳定区域的一种代数表达形式。最后给出了实例。     

控制理论中的频率定理 (Kalman-Yakubovich引理)*

频率定理（Ｋａｌｍａｎ－Ｙａｋｕｂｏｖｉｃｈ）是控制理论中的重要结果之一,它给出了Ｌｕｒ’ｅ方程和Ｒｉｃｃａｔｉ方程可解的一个充分必要条件,本文简要叙述了频率定理建立和发展的历史,描述了它在非线性系统绝对稳定性理论,线性二次型最优控制和自适应控制理论中的部分应用。     

凸锥型不确定线性切换系统的二次镇定

研究具有凸锥型不确定性的线性切换系统的二次鲁棒稳定化问题.这种不确定性是由若干已知常数矩阵所张成的凸锥构成的.利用凸组合技术,分别给出了连续和离散线性切换系统的鲁棒二次可稳定条件及切换律的设计方法.按照这些条件,只要判断张成凸锥的顶点矩阵的某个凸组合是否可稳即可.最后给出仿真例子.     

A new result on stability analysis for stochastic neutral systems

This paper discusses the mean-square exponential stability of stochastic linear systems of neutral type. Applying the Lyapunov–Krasovskii theory, a linear matrix inequality-based delay-dependent stability condition is presented. The use of model transformations, cross-term bounding techniques or additional matrix variables is all avoided, thus the method leads to a simple criterion and shows less conservatism. The new result is derived based on the generalized Finsler lemma (GFL). GFL reduces to the standard Finsler lemma in the absence of stochastic perturbations, and it can be used in the analysis and synthesis of stochastic delay systems. Moreover, GFL is also employed to obtain stability criteria for a class of stochastic neutral systems which have different discrete and neutral delays. Numerical examples including a comparison with some recent results in the literature are provided to show the effectiveness of the new results.     

一类新的Takagi-Sugeno模糊时滞系统的稳定性准则

本文提出一种新的时滞划分方法—变时滞划分法,以解决连续延时Takagi-Sugeno模糊系统的稳定性和镇定性问题.不同于已有的文献,用可变参数将时变时滞区间[0,d(t)]划分为若干个可变子区间,并得出模糊时滞系统的新的时滞相关稳定性准则.本文提出的新方法能充分利用时滞子区间的内部信息,因此新的时滞相关稳定性准则比以往结果具有更小的保守性.基于Lyapunov稳定性理论,以线性矩阵不等式形式给出T--S模糊系统的新的时滞相关稳定性准则,并将稳定性和镇定性研究结果扩展到具有不确定参数的T--S模糊系统.仿真实例证明了本文方法降低保守性的有效性.     

Robust controllability and observability degrees of polynomially uncertain systems

This paper deals with the class of polynomially uncertain continuous-time linear time-invariant (LTI) systems whose uncertainties belong to a semi-algebraic set. The objective is to determine the minimum of the smallest singular value of the controllability or observability Gramian over the uncertainty region. This provides a quantitative measure for the robust controllability or observability degree of the system. To this end, it is shown that the problem can be recast as a sum-of-squares (SOS) problem. In the special case when the uncertainty region is polytopic, the corresponding SOS formulation can be simplified significantly. One can apply the proposed method to any large-scale interconnected system in order to identify those inputs and outputs that are more effective in controlling the system, in a robust manner. This enables the designer to simplify the control structure by ignoring those inputs and outputs whose contribution to the overall control operation is relatively weak. A numerical example is presented to demonstrate the efficacy of the results.     

Robust stability of systems with both parametric and dynamic uncertainties

This paper studies the robust stability of a single-input–single-output systems with both parametric and dynamic uncertainties. The parametric uncertainties of the system are described by a polytopic perturbation mode, and the dynamic uncertainties are characterized by an integral quadratic constraint. Based on the concepts of biconvex and convex–concave functions and their properties, the problem of stability checking is discussed, and for different uncertainty structures of the system, the finite vertex-checking results and the edge-checking results are presented.     

不确定中立型系统鲁棒稳定及镇定的时滞相关准则

This paper concerns problem of the delay-dependent robust stability and stabilization for uncertain neutral systems. Some new delay-dependent stability criteria are derived by taking the relationship between the terms in the Leibniz-Newton formula into account. Free weighting matrices are given to express the relationship between the terms in the Leibniz-Newton formula and the new criteria are based on linear matrix inequalities such that the free weighting matrices can be easily obtained. Moreover, the stability criteria are also used to design the state-feedback controller. Numerical examples demonstrates that the proposed criteria are effective and are an improvement over the previous papers.     

A general method for function synthesis†

This paper proposes some mathematical relations that may be used to describe conditions in systems after connections have been altered. The common rules of conservation of charge and flux emerge as particular instances of these more general relations. The results obtained apply in systems containing amplifiers (subject to model adequacy)—a case excluded by the normal conservation stipulations.

The conditions under which a peculiar form of instability is encountered are presented.     

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。