Article ID Journal Published Year Pages File Type
9503285 Journal of Mathematical Analysis and Applications 2005 6 Pages PDF
Abstract
The classical criterion of asymptotic stability of the zero solution of equations x′=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 −(|dVdt|+|d2Vdt2|+⋯+|dmVdtm|+|dm+pVdtm+p|) is negative definite.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
Authors
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