区间矩阵稳定的新充分必要条件

本文讨论了对称区间矩阵的稳定性并给出了一个简单的充分必要条件，同时还讨论了线性时变区间矩阵和非线性时变区间矩阵的稳定性。     

求解对称区间矩阵标准特征值的进化策略新算法

针对实对称区间矩阵的特征值问题,将区间不确定量看成是围绕区间中点的一种摄动,提出了一种基于区间扩张的对称区间矩阵特征值问题求解的进化策略算法。将区间矩阵中点作为平衡点,区间不确定量作为相应的扰动量,根据摄动公式求出区间矩阵的最大特征值和最小特征值,从而获得区间矩阵特征值问题的解。算例显示了该算法的有效性,其主要特点是收敛速度快、求解区间精度高。     

关于时变区间矩阵的稳定性研究

本文对无界时变区间矩阵Ｎ［ Ｐ（ｔ），Ｑ（ｔ）］的稳定性进行了研究，给出了无界时 对变区间矩阵和具有分解的时变区间矩阵Ｎ［Ｐ（ｔ），Ｑ（ｔ）］稳定的充分条件，推广和改进了文［１，２］的工作。     

区间数判断矩阵满意一致性的判定方法和方案的排序

研究区间数判断矩阵的满意一致性和方案的排序.首先,给出区间数判断矩阵满意一致性的一种新的定义;然后,利用区间数判断矩阵的0-1型中心值排列矩阵是否为标准0-1型排列矩阵来判断区间数判断矩阵是否为满意一致性矩阵,若具有满意一致性,则可以直接从0-1型中心值排列矩阵中得出方案的优劣顺序,此种方法适用于对存在等价方案的区间数判断矩阵满意一致性的判定;最后给出两个例子说明了该方法的合理性和可行性.     

区间矩阵的鲁棒稳定性判据

基于一种非线性的幂变换,将区间矩阵的鲁棒稳定性问题转化成相应参数矩阵的非奇异性问题,并结合Gershgorin圆盘定理,得到了保证系统鲁棒稳定的充分条件。该判据对矩阵元素没有任何附加要求,简单而且实用。最后通过实例论证了所给判据的有效性。     

广义区间动力系统脉冲模存在性判据

系统有无脉冲行为直接影响到系统性质,本文针对广义区间动力系统首先给出了区间矩阵奇异值变化范围的判定定理,然后得到判别区间矩阵秩的变化范围的充分条件,进而得到判别广义区间动力系统具有脉冲模的判据.     

区间矩阵稳定的充分条件

本文讨论了几类元素不确定区间矩阵的稳定性问题,得到了若干充分判据,改进了对称区间矩阵稳定性的结果。     

区间粗糙数互补判断矩阵的两种一致性

区间粗糙数判断矩阵具有在不确定判断中保留部分确定判断的双重特性，然而目前对其研究相对较少，特别是对其一致性的相关研究。为此该文提出了区间粗糙数互补判断矩阵的完全一致性和强一致性的概念以及判断其是否具有完全一致性和强一致性的相关定理。通过算例讨论了内外一致性对于整体一致性的影响，并给出区间粗糙数判断矩阵的完全一致性和强一致性的关系，为区间粗糙数判断矩阵的应用提供一致性理论基础作出相应探讨。     

关于区间矩阵的稳定性

文献[1]试图给出由端点矩阵的稳定性来保证区间矩阵的稳定性,文[2,3]指出文[1]的主要结果是错的.本文给出了端点矩阵的稳定性在一定条件下可以保证区间矩阵的稳定性,其结果比文[4]更精确,适用范围更大,且对具有分解的区间矩阵给出了其稳定及不稳定的充分条件.     

区间互补判断矩阵可接受一致性

对区间互补判断矩阵的一致性进行研究,提出一种新的可接受一致性定义,将不满足可接受一致性的矩阵较容易地修正为可接受一致性矩阵.基于凸组合方法,一族明晰数互补判断矩阵的权重向量可被用来求取可接受一致性区间互补判断矩阵的区间权重,并提出了求取可接受一致性区间互补判断矩阵区间权重向量的算法.数值例子显示了所提出的可接受一致性定义以及算法的可行性和有效性.     

An efficient methodology for robust control of dynamic systems with interval matrix uncertainties

Interval models are frequently used for dealing with uncertainties of control systems. However, it is well known that direct analysis and synthesis of a controlled dynamic system with interval matrix uncertainties may be a NP-hard problem. In this work, an efficient methodology for robustness analysis and robust control design of dynamic systems with interval matrix uncertainties is presented systematically, in which the uncertainties appearing in the controlled plant and controller realisation are taken into account simultaneously in an integrated framework. The fundamental problems, such as quadratic stability, guaranteed cost control and H_∞ control of uncertain systems are taken as examples to show the methodology. Necessary and sufficient conditions for linear dynamic systems with interval matrices are derived by transforming all the interval matrices into some more tractable forms. The whole reasoning process is logical and rigorous, and NP-hard problem is successfully avoided. The presented formulations are within the framework of linear matrix inequality and can be implemented conveniently. In contrast to existing vertex-set methods, in which the vertices of interval matrices need to be constructed and checked, the presented methods are more efficient. Three numerical examples are investigated to demonstrate the effectiveness and feasibility of the presented method.     

A Kharitonov-like theorem for interval polynomial matrices

As an extension of Kharitonov's theorem, robust stability of interval polynomial matrices is studied. Here a polynomial matrix is said to be stable if its determinant has all roots with negative real parts. The present paper shows that the robust stability of interval polynomial matrices is equivalent to that of the subclasses where each row (column) has only one element that involves Kharitonov edge polynomials and all the other elements take on one of the four Kharitonov vertex polynomials.     

区间矩阵二次稳定的充分必要条件

提出了区间矩阵二次稳定的充分必要条件,以及相应的稳定裕度的计算方法.结论以线性矩阵不等式(LMI)的形式给出.利用功能强大的LMI工具,求解非常方便.所给实例表明,该方法用于确定区间矩阵的鲁棒稳定性及其稳定裕度,非常有效.     

Fault detection for discrete-time LPV systems using interval observers

This paper is concerned with the fault detection (FD) problem for discrete-time linear parameter-varying systems subject to bounded disturbances. A parameter-dependent FD interval observer is designed based on parameter-dependent Lyapunov and slack matrices. The design method is presented by translating the parameter-dependent linear matrix inequalities (LMIs) into finite ones. In contrast to the existing results based on parameter-independent and diagonal Lyapunov matrices, the derived disturbance attenuation, fault sensitivity and nonnegative conditions lead to less conservative LMI characterisations. Furthermore, without the need to design the residual evaluation functions and thresholds, the residual intervals generated by the interval observers are used directly for FD decision. Finally, simulation results are presented for showing the effectiveness and superiority of the proposed method.     

区间分数阶系统的鲁棒稳定性判别准则:0 < α < 1

针对同元阶次在0和1之间的区间分数阶系统,提出了类似Kharitonov定理的鲁棒稳定性判别准则. 研究了区间分数阶系统分母的主分支函数值集不包含原点所需满足的条件.根据除零原理, 给出了区间分数阶系统鲁棒稳定的顶点和棱边条件. 定义了由分母函数系数构成的矩阵,通过检验矩阵是否在负实轴上存在特征值来检验棱边条件. 最后,通过对两个数值算例的分析说明了这种方法的有效性.     

Design of functional interval observers for non‐linear fractional‐order systems

This paper considers the problem of designing functional interval observers for a class of non‐linear fractional‐order systems with bounded uncertainties. First, interval observers for linear functions of the state vector of the considered system are designed. Then, conditions for the existence of such interval observers are established and an effective algorithm for computing unknown observer matrices is provided in this paper. Finally, numerical examples and simulation results are given to illustrate the effectiveness of the proposed design method.     

Parallel Solutions for Large-Scale General Sparse Nonlinear Systems of Equations

In solving application problems,many large-scale nonlinear systems of equaions result in sparse Jacobian matrices.Such nonlinear systems are called sparse nonlinear systems.The irregularity of the locations of nonzrero elements of a general sparse matrix makes it very difficult to generally map sparse matrix computations to multiprocessors for parallel processing in a well balanced manner.To overcome this difficulty,we define a new storage scheme for general sparse matrices in this paper,With the new storage scheme,we develop parallel algorithms to solve large-scale general sparse systems of equations by interval Newton/Generalized bisection methods which reliably find all numerical solutions within a given domain.I n Section 1,we provide an introduction to the addressed problem and the interval Newton‘s methods.In Section 2,some currently used storage schemes for sparse systems are reviewed.In Section 3,new index schemes to store general sparse matrices are reported.In Section 4,we present a parallel algorithm to evaluate a general sparse Jacobian matrix.In Section 5,we present a parallel algorithm to solve the corresponding interval linear system by the all-row preconditioned scheme.Conclusions and future work are discussed in Section 6.