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.     

离散区间系统的二次稳定性及其稳定裕度分析

研究了动态离散区间系统的鲁棒稳定性问题,提出了系统二次稳定的充分与必要条件,以及相应的稳定裕度的计算方法,并推广到离散参数不确定系统.所有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,该方法用于确定动态离散区间系统的鲁棒稳定性及其稳定裕度,非常有效.     

Stabilization of perturbed systems via linear optimal regulator

Linear quadratic state feedback regulators make the resulting closed-loop systems stable enough, i.e. they realize robust stabilization. Many attempts at robust stabilization using linear quadratic regulators have been reported. One of the major trends of formulating uncertainty in systems is to express perturbed parameters as the sum of two terms, i.e. nominal values and the deviation from them. In this paper, it is assumed that the upper and lower bounds for each uncertain parameter can somehow be estimated. This enables us to dispense with nominal values. The main aim is to contrive a robust feedback stabilization law for systems with parameters falling into certain ranges via a linear quadratic regulator based only upon information on their bounds. The systems under consideration are therefore those having interval system matrices (in which each element has the above-mentioned two-sided bounds). A certain feedback law is a stabilizing law for a system with an interval system matrix if and only if the same feedback law remains so for systems with system matrices whose entries are all possible combinations of the endpoints of their variation range.     

一类不确定系统的鲁棒D-稳定保守性研究

针对一类多面体不确定线性连续系统,研究了系统鲁棒D-稳定问题.为降低设计的保守性,引入参数相关Lyapunov函数,给出了系统鲁棒D-稳定的充分条件.通过求解一组线性矩阵不等式,得到了系统鲁棒D-稳定的状态反馈控制器,使得闭环系统鲁棒D-稳定.对某卫星姿态控制系统的仿真结果表明了该方法的有效性.     

Piecewise Lyapunov functions for robust stability of linear time-varying systems

In this paper, we investigate the use of two-term piecewise quadratic Lyapunov functions for robust stability of linear time-varying systems. By using the so-called S-procedure and a special variable reduction method, we provide numerically efficient conditions for the robust asymptotic stability of the linear time-varying systems involving the convex combinations of two matrices. An example is included to demonstrate the usefulness of our results.     

New results on robust exponential stability of integral delay systems

The robust exponential stability of integral delay systems with exponential kernels is investigated. Sufficient delay-dependent robust conditions expressed in terms of linear matrix inequalities and matrix norms are derived by using the Lyapunov–Krasovskii functional approach. The results are combined with a new result on quadratic stabilisability of the state-feedback synthesis problem in order to derive a new linear matrix inequality methodology of designing a robust non-fragile controller for the finite spectrum assignment of input delay systems that guarantees simultaneously a numerically safe implementation and also the robustness to uncertainty in the system matrices and to perturbation in the feedback gain.     

LMI Condition of Quadratic D-stability for a Class of Uncertain Linear Systems

A necessary and sufficient condition of the quadratic D-stability for a class of uncertain linear systems is presented in terms of linear matrix inequality (LMI) technology.Finally,the validity and less conservatism of the obtained results in this paper are illustrated by a benchmark example.     

A new discrete-time robust stability condition

A new robust stability condition for uncertain discrete-time systems with convex polytopic uncertainty is given. It enables to check stability using parameter-dependent Lyapunov functions which are derived from LMI conditions. It is shown that this new condition provides better results than the classical quadratic stability. Besides the use of a parameter-dependent Lyapunov function, this condition exhibits a kind of decoupling between the Lyapunov and the system matrices which may be explored for control synthesis purposes. A numerical example illustrates the results.     

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.     

具有时变不确定性的脉冲时滞大系统的鲁棒稳定性

提出并研究了具有时变不确定性的脉冲时滞大系统的鲁棒稳定性,借助于向量比较原理和矩阵不等式等方法,对该系统建立了若干大范围指数鲁棒稳定的判据,并举例说明了结论的有效性。     

Criteria for robust absolute stability of time-varying nonlinear continuous-time systems

The present paper establishes results for the robust absolute stability of a class of nonlinear continuous-time systems with time-varying matrix uncertainties of polyhedral type and multiple time-varying sector nonlinearities. By using the variational method and the Lyapunov Second Method, criteria for robust absolute stability are obtained in different forms for the given class of systems. Specifically, the parametric classes of Lyapunov functions are determined which define the necessary and sufficient conditions of robust absolute stability. The piecewise linear Lyapunov functions of the infinity vector norm type are applied to derive an algebraic criterion for robust absolute stability in the form of solvability conditions of a set of matrix equations. Several simple sufficient conditions of robust absolute stability are given which become necessary and sufficient for special cases. Two examples are presented as applications of the present results to a particular second-order system and to a specific class of systems with time-varying interval matrices in the linear part.     

一类不确定线性系统二次D-稳定的LMI条件

A necessary and sufficient condition of the quadratic D-stability for a class of uncertain linear systems is presented in terms of linear matrix inequality (LMI) technology. Finally, the validity and less conservatism of the obtained results in this paper are illustrated by a benchmark example.     

Characterization of robust stability of a class of interconnected systems

We consider robust stability analysis of a class of large scale interconnected systems. The individual subsystems may be different but they are assumed to share a property that characterizes a set of interconnection matrices which lead to stable overall systems. The main contribution of the paper is to show that, for the case where the network interconnection matrix is normal, (robust) stability verification can be simplified to a low complexity problem of checking whether the frequency response of the individual subsystems and the eigenvalues of the interconnection matrix can be mutually separated using a class of quadratic forms. Most interestingly, it is shown that this criterion is also necessary, in the sense that if the criterion is violated, an interconnection matrix of the same eigenvalue distribution can be found to make the overall system unstable.     

On relationship between quadratic and robust stability of uncertain systems

A game theoretic approach is introduced to analyse the relationship between the quadratic and robust stability of systems with structured uncertainties. Necessary and sufficient condition for the equivalence of these two types of stability is presented. The distance between quadratic and robust stability is bounded when this condition is not satisfied. This gives new insight into the mechanism of the quadratic stability. Checking this necessary and sufficient condition and calculating the error bound are formulated as a convex optimization problem. The results developed in this paper are illustrated by several numerical examples. Copyright © 1999 John Wiley & Sons, Ltd.     

多项式理论在导弹稳定性能评估中的应用

针对线性参数不确定性系统的鲁棒稳定性问题,提出一种新的分析方法,并对其在导弹自动驾驶仪鲁棒稳定性评估中的可行性进行了研究。首先给出线性参数不确定性系统在其特征多项式系数不相关情况下的鲁棒稳定性的充要条件,并通过自适应网格划分算法将此条件与鲁棒D-稳定性理论结合,得到基于多项式理论的评估算法。将算法用于导弹自动驾驶仪鲁棒稳定性评估,得到了不同攻角下导弹在全包线范围内的稳定区域。和只能在离散点进行评估的传统评估方法比较,结果表明提出的算法可以在全包线范围内连续进行评估,从而发现一些隐蔽的不稳定区域。     

广义不确定周期时变系统的鲁棒稳定性分析

研究广义不确定周期时变系统的鲁棒稳定性问题.基于广义周期时变系统Lyapunov不等式,提出了广义不确定周期时变系统鲁棒稳定的概念,采用矩阵不等式(LMI)方法,得到了该类系统鲁棒稳定的充分必要条件;然后,进一步研究了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;最后,引入了广义周期时变系统二次稳定的概念,并讨论了二次稳定性与鲁棒稳定性之间的关系.     

Stability robustness of interval matrices via Lyapunov quadraticforms

A sufficient condition for the robust stability of a class of interval matrices is derived using the Lyapunov approach. The matrices considered have elements which are nonlinear functions of a vector of independent and bounded parameters. The robust stability condition requires that a quadratic form be positive definite in a finite number of conspicuous points of an enlarged parameter space     

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，     

Robust D-Stability Test of LTI General Fractional Order Control Systems

This work deals with the robust D-stability test of linear time-invariant(LTI) general fractional order control systems in a closed loop where the system and/or the controller may be of fractional order. The concept of general implies that the characteristic equation of the LTI closed loop control system may be of both commensurate and non-commensurate orders, both the coefficients and the orders of the characteristic equation may be nonlinear functions of uncertain parameters, and the coefficients may be complex numbers. Some new specific areas for the roots of the characteristic equation are found so that they reduce the computational burden of testing the robust D-stability. Based on the value set of the characteristic equation, a necessary and sufficient condition for testing the robust D-stability of these systems is derived. Moreover, in the case that the coefficients are linear functions of the uncertain parameters and the orders do not have any uncertainties, the condition is adjusted for further computational burden reduction. Various numerical examples are given to illustrate the merits of the achieved theorems.