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Stability Analysis in Terms of Two Measures for Impulsive Differential Equations
Author(s) -
Kou Chunhai,
Zhang Shunian,
Wu Shujin
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003277
Subject(s) - instability , perturbation (astronomy) , mathematics , lyapunov function , stability theory , differential equation , stability (learning theory) , variable (mathematics) , mathematical analysis , control theory (sociology) , computer science , nonlinear system , physics , mechanics , control (management) , quantum mechanics , machine learning , artificial intelligence
Through the use of the so‐called variational Lyapunov method, which is developed by combining the method of variation of parameters and the Lyapunov second method, stability and instability properties in terms of two measures for impulsive differential equations with variable moments of impulsive effects are discussed. Some stability and instability criteria are established. These theorems, together with an example, show that perturbation and impulsive effects may make a stable system uniformly asymptotically stable or unstable. These results significantly generalize the known ones.