Stability and asymptotic estimates in nonautonomous linear differential systems

G. Söderlind; R.M.M. Mattheij

doi:10.1137/0516005

Stability and asymptotic estimates in nonautonomous linear differential systems

G. Söderlind, R.M.M. Mattheij

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

348 Downloads (Pure)

Abstract

A new theory is presented, in which a generalized kinematic similarity transformation is used to diagonalize linear differential systems. No matrices of Jordan form are needed. The relation to Lyapunov’s classical stability theory is explored, and asymptotic estimates of fundamental solutions are given. Finally, some possible numerical applications of the presented theory are suggested.

Original language	English
Pages (from-to)	69-92
Journal	SIAM Journal on Mathematical Analysis
Volume	16
Issue number	1
DOIs	https://doi.org/10.1137/0516005
Publication status	Published - 1985

Access to Document

10.1137/0516005

Metis187911Final published version, 2.16 MB

Cite this

@article{0909955ca511443bb9ed32a145239da6,

title = "Stability and asymptotic estimates in nonautonomous linear differential systems",

abstract = "A new theory is presented, in which a generalized kinematic similarity transformation is used to diagonalize linear differential systems. No matrices of Jordan form are needed. The relation to Lyapunov{\textquoteright}s classical stability theory is explored, and asymptotic estimates of fundamental solutions are given. Finally, some possible numerical applications of the presented theory are suggested.",

author = "G. S{\"o}derlind and R.M.M. Mattheij",

year = "1985",

doi = "10.1137/0516005",

language = "English",

volume = "16",

pages = "69--92",

journal = "SIAM Journal on Mathematical Analysis",

issn = "0036-1410",

publisher = "Society for Industrial and Applied Mathematics (SIAM)",

number = "1",

}

TY - JOUR

T1 - Stability and asymptotic estimates in nonautonomous linear differential systems

AU - Söderlind, G.

AU - Mattheij, R.M.M.

PY - 1985

Y1 - 1985

N2 - A new theory is presented, in which a generalized kinematic similarity transformation is used to diagonalize linear differential systems. No matrices of Jordan form are needed. The relation to Lyapunov’s classical stability theory is explored, and asymptotic estimates of fundamental solutions are given. Finally, some possible numerical applications of the presented theory are suggested.

AB - A new theory is presented, in which a generalized kinematic similarity transformation is used to diagonalize linear differential systems. No matrices of Jordan form are needed. The relation to Lyapunov’s classical stability theory is explored, and asymptotic estimates of fundamental solutions are given. Finally, some possible numerical applications of the presented theory are suggested.

U2 - 10.1137/0516005

DO - 10.1137/0516005

M3 - Article

SN - 0036-1410

VL - 16

SP - 69

EP - 92

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 1

ER -

Stability and asymptotic estimates in nonautonomous linear differential systems

Abstract

Access to Document

Fingerprint

Cite this