The structured distance to non-surjectivity and its application to calculating the controllability radius of descriptor systems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:388

Article

Nguyen Khoa Son¹  Do Duc Thuan² 

[1] Vietnam Acad Sci & Technol, Inst Math, Hanoi 10307, Vietnam

[2] Hanoi Univ Technol, Dept Appl Math & Informat, Hanoi, Vietnam

关键词: Multi-valued linear operators;    Distance to non-surjectivity;    Descriptor systems;    Distance to uncontrollability;    Structured perturbations;    Multi-perturbations;   

DOI  :  10.1016/j.jmaa.2011.10.005

来源: Elsevier

【 摘 要 】

The classical Eckart-Young formula for square matrices identifies the distance to singularity of a matrix. The main purpose of this paper is to get generalizations of this formula. We characterize the distance to non-surjectivity of a linear operator W is an element of L(X, Y) in finite-dimensional normed spaces X, Y, under the assumption that the operator W is surjective (i.e. W X = Y) and subjected to structured perturbations of the form W + M Delta N. As an application of these results, we shall derive formulas of the controllability radius for a descriptor controllable system [E, A, B]: E(x) over dot = Ax + Bu, t >= 0, under the assumption that systems matrices E, A. B are subjected to structured perturbations and to multi-perturbations. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free