Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9503285 | Journal of Mathematical Analysis and Applications | 2005 | 6 Pages |
Abstract
The classical criterion of asymptotic stability of the zero solution of equations xâ²=f(t,x) is that there exists a positive definite function V which has infinitesimal upper bound such that dVdt is negative definite. In this paper we prove that if dm+1Vdtm+1 is bounded then the condition that dVdt is negative definite can be weakened and replaced by that dVdt⩽0 and â(|dVdt|+|d2Vdt2|+â¯+|dmVdtm|+|dm+pVdtm+p|) is negative definite.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Liangping Jiang,