On the D-stability and additive D-stability of matrices and Svicobians

被引：0

作者：

Kosov A.A. ^{[1
]}

机构：

[1] Institute of System Dynamics and Control Theory, Irkutsk 664033

来源：

Journal of Applied and Industrial Mathematics | 2010年 / 4卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

Additive D-stability; D-stability; Matrix; Stability in the sense of Lyapunov;

D O I：

10.1134/S1990478910020092

中图分类号：

学科分类号：

摘要：

We improve the available necessary conditions and sufficient conditions for the Dstability and additive D-stability of matrices. We define these dynamical properties with respect to a finite parallelepiped and propose an algorithm for checking them. For a particular class of matrices called Svicobians, we obtain some constructive necessary and sufficient conditions for Dstabilizability, D-stability, and additive D-stability. © 2010 Pleiades Publishing, Ltd.

引用

页码：200 / 212

页数：12

共 12 条

[1]

Romanishin I.M., Sinitskii L.A., On the Additive D-Stability of Matrices on the Basis of the Kharitonov Criterion, Mat. Zametki, 72, 2, pp. 265-268, (2002)

[2]

Kanovei G.V., Logofet D.O., D-Stability of 4 × 4 Matrices, Zh. Vychisl. Mat. I Mat. Fiz., 38, 9, pp. 1429-1435, (1999)

[3]

Impram S., Johnson R., Pavani R., The D-Stability Problem for 4 × 4 Real Matrices, Arch. Math. (Brno), 41, pp. 439-450, (2005)

[4]

Logofet D.O., Svicobians of Compartment Models and the DaD-Stability of Svicobians, Dokl. Akad. Nauk, Ross. Akad. Nauk, 360, 2, pp. 167-170, (1998)

[5]

Svirezhev Y.M., Logofet D.O., Stability of Biological Communities, (1978)

[6]

Pykh Y.A., Equilibrium and Stability in the Models of Population Dynamics, (1983)

[7]

Aleksandrov A.Y., Platonov A.V., Starkov V.N., Stepenko N.A., Mathematical Modeling and Study of Stability of Biological Communities, (2006)

[8]

Kharitonov V.L., Asymptotic Stability of an Equilibrium Position of a Family of Systems of Linear Differential Equations, Differentsial'nyeUravneniya, 14, 11, pp. 2086-2088, (1978)

[9]

Gantmakher F.R., The Theory of Matrices, (1988)

[10]

Godunov S.K., Problem of the Dichotomy of the Spectrum of a Matrix, Sibirsk. Mat. Zh., 27, 5, pp. 24-37, (1986)

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