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1.
蔡晨晓  邹云 《自动化学报》2007,33(5):511-517
讨论了关于离散奇异摄动系统的摄动稳定性解析条件, 给出了离散奇异摄动系统两种模型下的摄动稳定性充要条件. 通过分析状态矩阵的结构特性, 得出了系统稳定所需要的状态矩阵形式和限制条件. 同时, 通过广义系统途径也得到了 2-D 离散奇异摄动 Roessor 模型稳定的充分条件.  相似文献   

2.
Parametric uncertainties in linear time-invariant state-space models introduce perturbations in the eigenvalues and eigenvectors (eigenstructure), which modify the properties of a nominal system. Besides stability by the perturbed eigenvalues, controllability, observability, transient and steady-state values, etc., are some basic properties of a linear system significantly influenced by the perturbed eigenvectors. In this paper, time response analysis of parametric uncertain systems is considered. First the bounds on eigenvectors and parametric uncertainties are established for the perturbed eigenvalues to reside in a set of distinct circular regions. Secondly, analysis of such parametric uncertain systems is discussed by presenting bounds on the perturbed state variables in time coordinate. These bounds are then investigated for norm-bounded and structured uncertainty classifications. Input-output analysis of uncertain systems is illustrated using the initial conditions and input functions.  相似文献   

3.
Recently, Martin and Hewer (1987) have given a measure of the ‘size of the smallest’ perturbation E that renders a perturbed linear system unstable. These results require global minimization which is computationally difficult. Two conditions are derived which guarantee the stability of a perturbed linear system. These conditions do not require global minimization.  相似文献   

4.
The controllability and the observability of continuous linear time-varying systems with norm-bounded parameter perturbations are analyzed. The sufficient conditions which ensure the controllability of the perturbed system are presented by using the derived state transition matrix relationship between the nominal system and the perturbed system. The proposed sufficient conditions allow the evaluation of controllability under the norm-bounded parameter perturbations. The robustness of the observability is also studied for continuous linear time varying systems with norm-bounded parameter perturbations, and the corresponding sufficient conditions are provided  相似文献   

5.
Robust stability conditions are considered for linear perturbed large-scale systems with saturating actuators in the discrete-time case. Both non-linear and linear perturbations are considered. Two types of controllers, a state feedback and a dynamic controller, are introduced for each sub-system to guarantee asymptotic stability of the perturbed large-scale system.  相似文献   

6.
This paper is concerned with the robust stability conditions for linear perturbed systems with saturating actuators in the discrete-time case. Both non-linear and linear perturbations are considered. Two types of controller, a state feedback and a dynamic controller, are introduced to guarantee asymptotic stability of the perturbed system.  相似文献   

7.
In this note we study the global null controllability with bounded controls of perturbed linear periodic systems in Rn. More explicitly, a globally null controllable periodic system is perturbed by suitably small termsV(t)andC(t)to obtain a system of the formdot{x} = (A(t) + V(t))x + (B(t) + C(t))uand sufficient conditions are given to ensure the global null controllability of the resulting perturbed system.  相似文献   

8.
A method is presented for modeling a two-time-scale system in the singularly perturbed form. The method uses an ordered real Schur decomposition, which can be efficiently computed using standard subroutines from EISPACK. Three results are given. First, it is shown that any two-time-scale system can be modeled in the singularly perturbed form by a transformation into an ordered real Schur form, followed by balancing. Second, under some conditions on the ordered real Schur decomposition, a procedure is given to achieve the modeling task with all fast variables chosen from the original state variables. Third, necessary and sufficient conditions are given to achieve modeling by permutation of the original state variables  相似文献   

9.
把微扰力学系统视为未受微扰系统与微扰项的迭加,并选择合适的方法求得未受微扰系统的精确守恒量I0.从近似守恒量的性质出发,建立守恒量的一阶微扰项系数I1与精确守恒量I0、守恒量的二阶微扰项系数I2与守恒量的一阶微扰项系数I1及精确守恒量I0的递推关系.考虑微扰项对精确守恒量以及对守恒量的一阶微扰项系数的影响,利用递推关系并直接积分求得二阶近似守恒量.文中用此方法研究了一微扰力学系统的二阶近似守恒量,并得到2个稳定的二阶近似守恒量.  相似文献   

10.
Stability robustness measures for a perturbed linear feedback system are derived based on state-space models of the system. The system may be a continuous-time or discrete-time system. The perturbations are modeled as additive perturbation matrices. Necessary and sufficient conditions for the stability of the perturbed closed-loop system for all perturbations of norm bounded by some positive number are obtained. The destabilizing perturbations of minimal norm are characterized. It is shown by an example that there are cases when the destabilizing perturbations of minimal norm are all complex. The results are expressed in terms of induced operator norms. These are later specialized to the Euclidean norm and expressed in terms of singular values. A simple example is also included to illustrate an application of the results of this note.  相似文献   

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