DocumentCode :
807531
Title :
Instability of slowly varying systems
Author :
Skoog, Ronald A. ; Lau, Clifford G Y
Author_Institution :
Bell Telephone Laboratories, Holmdel, NJ, USA
Volume :
17
Issue :
1
fYear :
1972
fDate :
2/1/1972 12:00:00 AM
Firstpage :
86
Lastpage :
92
Abstract :
Instability criteria are obtained for systems described by 
when the parameters are slowly varying. In particular it is shown that, when 
has eigenvalues in the right-half plane and all eigenvalues are bounded away from the imaginary axis, then if 
is sufficiently small, the system has unbounded solutions. Results are also given for systems of the form 
, and the dichotomy of solutions is studied in both the linear and nonlinear cases.
when the parameters are slowly varying. In particular it is shown that, when has eigenvalues in the right-half plane and all eigenvalues are bounded away from the imaginary axis, then if is sufficiently small, the system has unbounded solutions. Results are also given for systems of the form , and the dichotomy of solutions is studied in both the linear and nonlinear cases.Keywords :
Linear systems, time-varying continuous-time; Stability; Eigenvalues and eigenfunctions; Equations; Laboratories; Lyapunov method; Nonlinear systems; Stability criteria; Vectors;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1972.1099866
Filename :
1099866
Link To Document :
