线性状态空间模型的稳定鲁棒性改善

本文讨论线性定常系统的稳定鲁棒性问题。文中给出了线性定常系统的稳定鲁棒性范围的新改善界限。在结构扰动情况下，本文给出的稳定鲁棒性界限比引文[1]中的相应结果更好。用数值计算方法容易得到这一动扰界限。文中给出的两个例子证实了本文结果的优点。     

灰色系统稳定性充分条件及其在线性时变系统稳定性分析中的应用

本文利用非负不可约矩阵的性质分析了灰色线性定常系统的稳定性问题,给出了灰色线性定常系统稳定性充分判据。所得判据不仅可用来分析灰色线性定常系统的稳定性,而且可用来分析线性时变系统的稳定性。作为所得判据的应用实例,本文还给出了确保线性时变系统稳定的充分条件。借此,可使很大一类线性时变系统的稳定性判定问题变得十分简单。     

离散线性时变系统稳定性研究

本文对离散线性时变系统的稳定性问题进行了研究。给出离散线性定常系统收敛速度的定义，基于离散线性时变系统Lyapunov稳定理论，给出离散线性时变系统稳定的充分条件，即系统系数满足系数冻结条件和系数变化条件。仿真验证了结论的正确性。     

一类不确定中立型系统的时滞相关稳定准则

本文讨论了一类定常系数时变时滞中立型系统的时滞相关稳定性. 以线性矩阵不等式形式给出了新的时滞相关渐近稳定标准. 二个数值例子表明本文结果比先前结论有较小的保守性.     

离散时滞大系统的无条件稳定性

本文研究一类线性定常离散时滞大系统的无条件稳定性问题。首先利用m阵的性质,给出了一般离散时滞系统无条件渐近稳定的充分条件;接着建立了适应于离散时滞系统的比较原理,最后用向量李雅普诺夫函数法和集结(aggregatioa)方法,推得了线性定常离散时滞大系统无条件稳定的充分条件。这一条件归结为判定一个阶数等于子系统个数的实矩阵是否是一个m阵。一个简单的数值例子说明了本文得出的结果的应用。     

线性连续时间系统的鲁棒自适应控制*

本文解决了参数未知，具有非结构性未建模误差和有界恒定扰动的一类线性连续统的自适应控制问题。文中给出的自适应控制器对上述干扰具有鲁棒性，它能保证自适应系统的稳定运行无奇异性产生。     

离散时间系统的定常状态估计器

本文研究线性定常离散时间系统当系统噪声和测量噪声为平稳白噪声序列时,为改进稳态Kalman滤波器瞬态性能的定常状态估计器的设计方法。文中提出了滤波器瞬态性能的度量方法;提出了两种新的性能函数的定义,从而给出两种瞬态性能得到改善的、适用于短时间运行的定常状态估计器。     

基于特征系数灵敏度的鲁棒极点配置

极点配置是控制理论课程中的重要内容,鲁棒性是衡量线性定常控制系统稳定性能的重要指标.文中提出了一种解决具有不确定性参数线性系统的鲁棒极点配置问题的方法,其中系统鲁棒性的指标采用加权的特征系数灵敏度,目标函数的求解采用标准的具有二次收敛性质的参数最优化方法.设计实例证实了该方法的可行性,故可作为控制理论课程的实际教学.     

多变量系统鲁棒性复数极点配置的一种新方法*

本文对线性定常多变量系统的鲁棒性极点配置问题,给出了一种算法。这个算法对指定闭环极点中含共轭复极点的情形,用起来十分方便,它把一个带约束优化问题变成了一个无约束优化问题求解,本文末还给出了一个数值例子。     

输出反馈鲁棒调节器设计

本文提出了受扰线性定常多变量系统的鲁棒调节器问题,利用区间矩阵的概念和输出反馈方法来设计鲁棒控制系统,通过兼容Riccati方程和方程解的方法,使系统既具有稳定鲁棒性,又能满足给定相对稳定性的要求。     

The stability robustness determination of state space models with real unstructured perturbations

This paper considers the robust stability of a linear time-invariant state space model subject to real parameter perturbations. The problem is to find the distance of a given stable matrix from the set of unstable matrices. A new method, based on the properties of the Kronecker sum and two other composite matrices, is developed to study this problem; this new method makes it possible to distinguish real perturbations from complex ones. Although a procedure to find the exact value of the distance is still not available, some explicit lower bounds on the distance are obtained. The bounds are applicable only for the case of real plant perturbations, and are easy to compute numerically; if the matrix is large in size, an iterative procedure is given to compute the bounds. Various examples including a 46th-order spacecraft system are given to illustrate the results obtained. The examples show that the new bounds obtained can have an arbitrary degree of improvement over previously reported ones. This work has been supported by the Natural Sciences and Engineering Research Council of Canada under Grant No. A4396.     

Robustness of pole-assignment in a specified region

An analysis of pole-assignment is given for systems under linear time-invariant perturbations. Based upon the Lyapunov approach, new techniques to calculate allowable element bounds for highly structured perturbations are presented. Under these allowable perturbations both stability robustness and a certain performance robustness are thus ensured. Examples are given to illustrate the proposed methods     

New robustness bounds for discrete systems with randomperturbations

Some new stochastic stability robustness bounds for state-space models are reported. Nominally exponentially stable discrete-time systems are assumed to be subject to random parameter perturbations and novel bounds are obtained on the maximum variances of these random perturbations to maintain stability robustness. The methods employed in the analysis are the existing ones used in the deterministic framework after transforming the stochastic robustness problem to a deterministic one. The results are compared with each other and with the exact stability region in an example     

Iterative algorithm for improved measures of stability robustness for linear state-space models

The problem of robust stability of linear lime-invariant systems in state-space models is considered. An iterative algorithm based on frequency domain approach is proposed which leads to new stability robustness measures. The case of structural perturbations is considered and the new bounds are shown to be a significant improvement over recent ones reported. In addition, it is shown that the directional information on structured perturbations can easily be incorporated in the new robustness criterion. Several illustrative examples are worked out.     

On the estimation of solution bounds of the generalized Lyapunov equations and the robust root clustering for the linear perturbed systems

This paper measures the solution bounds for the generalized Lyapunov equations (GLE). By making use of linear algebraic techniques, we estimate the upper and lower matrix bounds for the solutions of the above equations. All the proposed bounds are new, and it is also shown that the majority of existing bounds are the special cases of these results. Furthermore, according to these bounds, the problem of robust root clustering in sub-regions of the complex plane for linear time-invariant systems subjected to parameter perturbations is solved. The tolerance perturbation bounds for robust clustering in the given sub-regions are estimated. Compared to previous results, the feature of these tolerance bounds is that they are independent of the solution of the GLE.     

Robust stability of singularly perturbed discrete-delay systems

This paper presents new sufficient conditions for the robust stability of singularly perturbed discrete systems subjected to multiple delayed perturbations. For a given ε∈ [0, ε₀], where ε₀<ε*, a new criterion for finding the range of allowable bounds on the delayed perturbations is provided. A numerical example is given to illustrate the results     

Bounds on the solution of the algebraic Riccati equation under perturbations in the coefficients

This paper is concerned with bounds on symmetric solutions of the continuous algebraic matrix Riccati equation under perturbations on its coefficients. Special emphasis is given to the question of estimating the ‘size’ of the perturbations on the stabilizing solution of the Riccati equation when one or all its coefficients are subject to small perturbations. Upper bounds on the norm of the perturbations on the stabilizing solution are presented. Moreover, it is shown that these perturbations can be determined as a single-valued continuous function of the perturbations on the coefficient of the Riccati equation.     

Stability and robust stability of positive linear Volterra difference equations

We first introduce a class of positive linear Volterra difference equations. Then, we offer explicit criteria for uniform asymptotic stability of positive equations. Furthermore, we get a new Perron–Frobenius theorem for positive linear Volterra difference equations. Finally, we study robust stability of positive equations under structured perturbations and affine perturbations. Two explicit stability bounds with respect to these perturbations are given. Copyright © 2008 John Wiley & Sons, Ltd.     

Improved upper bounds for the mixed structured singular value

In this paper, we take a new look at the mixed structured singular value problem, a problem of finding important applications in robust stability analysis. Several new upper bounds are proposed using a very simple approach which we call the multiplier approach. These new bounds are convex and computable by using linear matrix inequality (LMI) techniques. We show, most importantly, that these upper bounds are actually lower bounds of a well-known upper bound which involves the so-called D-scaling (for complex perturbations) and G-scaling (for real perturbations)