The Stability Cone for a Matrix Delay Difference Equation-Reference-Cited by-同舟云学术

The Stability Cone for a Matrix Delay Difference Equation

Published:2011 Issue: Volume:2011 Page:1-15
ISSN:0161-1712
Container-title:International Journal of Mathematics and Mathematical Sciences
language:en
Short-container-title:International Journal of Mathematics and Mathematical Sciences

Author:

Kipnis M. M.¹,Malygina V. V.²

Affiliation:

1. Department of Mathematics, South Ural State University, Chelyabinsk 454080, Russia

2. Department of Applied Mathematics and Mechanics, Perm State Technical University, Perm 614990, Russia

Abstract

We construct a stability cone, which allows us to analyze the stability of the matrix delay difference equation . We assume that and are simultaneously triangularizable matrices. We construct points in which are functions of eigenvalues of matrices , such that the equation is asymptotically stable if and only if all the points lie inside the stability cone.

Publisher

Hindawi Limited

Subject

Mathematics (miscellaneous)

Link

http://downloads.hindawi.com/journals/ijmms/2011/860326.pdf

Reference19 articles.

1. A canonical parameter space for linear systems design

2. The Geometry of D-Decomposition of a Two-Dimensional Plane of Arbitrary Coefficients of the Characteristic Polynomial of a Discrete System

3. Stability of the Trinomial Linear Difference Equations with Two Delays

4. A note on explicit stability conditions for autonomous higher order difference equations

5. Convexity of the coefficient sequence and discrete systems stability

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