Open AccessStability implications on the asymptotic behavior of nonlinear systems
Author(s) -
Kuo-Liang Chiou
Publication year - 1982
Publication title -
international journal of mathematics and mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 39
eISSN - 1687-0425
pISSN - 0161-1712
DOI - 10.1155/s0161171282000106
Subject(s) - mathematics , nonlinear system , stability (learning theory) , combinatorics , existential quantification , pure mathematics , discrete mathematics , physics , computer science , quantum mechanics , machine learning
In this paper we generalize Bownds' Theorems (1) to the systems dY(t)dt=A(t)Y(t) and dX(t)dt=A(t)X(t)+F(t,X(t)). Moreover we also show that there always exists a solution X(t) of dXdt=A(t)X+B(t) for which limt→∞sup‖X(t)‖>o(=∞) if there exists a solution Y(t) for which limt→∞sup‖Y(t)‖>o(=∞)
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