Estimates for the norms of solutions of a perturbed linear dynamical system

Michael I. Gil'; Sui Sun Cheng

Estimates for the norms of solutions of a perturbed linear dynamical system

Michael I. Gil', Sui Sun Cheng

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

This paper is concerned with an nonautonomous perturbed linear dynamical system x_k+1 = Ax_k+Fk(x_k). A well known result of Perron states that this system is asymptotically stable if A is stable and that F_k(x)≡f(x)= o(∥x∥). It is clear that this is purely a local result which gives no information about the size of the region of asymptotic stability nor the size of the solutions. In this paper, estimates for the size of the solutions and regions of stability are derived.

Original language	English
Pages (from-to)	95-98
Number of pages	4
Journal	Proceedings of the National Science Council, Republic of China, Part A: Physical Science and Engineering
Volume	24
Issue number	2
State	Published - 1 Mar 2000

ASJC Scopus subject areas

General Engineering

Cite this

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title = "Estimates for the norms of solutions of a perturbed linear dynamical system",

abstract = "This paper is concerned with an nonautonomous perturbed linear dynamical system xk+1 = Axk+Fk(xk). A well known result of Perron states that this system is asymptotically stable if A is stable and that Fk(x)≡f(x)= o(∥x∥). It is clear that this is purely a local result which gives no information about the size of the region of asymptotic stability nor the size of the solutions. In this paper, estimates for the size of the solutions and regions of stability are derived.",

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AU - Cheng, Sui Sun

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N2 - This paper is concerned with an nonautonomous perturbed linear dynamical system xk+1 = Axk+Fk(xk). A well known result of Perron states that this system is asymptotically stable if A is stable and that Fk(x)≡f(x)= o(∥x∥). It is clear that this is purely a local result which gives no information about the size of the region of asymptotic stability nor the size of the solutions. In this paper, estimates for the size of the solutions and regions of stability are derived.

AB - This paper is concerned with an nonautonomous perturbed linear dynamical system xk+1 = Axk+Fk(xk). A well known result of Perron states that this system is asymptotically stable if A is stable and that Fk(x)≡f(x)= o(∥x∥). It is clear that this is purely a local result which gives no information about the size of the region of asymptotic stability nor the size of the solutions. In this paper, estimates for the size of the solutions and regions of stability are derived.

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M3 - Article

AN - SCOPUS:0034145048

SN - 0255-6588

VL - 24

SP - 95

EP - 98

JO - Proceedings of the National Science Council, Republic of China, Part A: Physical Science and Engineering

JF - Proceedings of the National Science Council, Republic of China, Part A: Physical Science and Engineering

IS - 2

ER -

Estimates for the norms of solutions of a perturbed linear dynamical system

Abstract

ASJC Scopus subject areas

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