On exponential stability of nonlinear time-varying differential equations

Within the Liapunov framework, a sufficient condition for exponential stability of ordinary differential equations is proposed. Unlike with classical Liapunov theory, the time derivative of the Liapunov function, taken along solutions of the system, may have positive and negative values. Verificatio...

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Bibliographic Details
Published in:Automatica (Oxford) 1999-06, Vol.35 (6), p.1091-1100
Main Authors: Aeyels, Dirk, Peuteman, Joan
Format: Article
Language:English
Subjects:
Applied sciences
Averaging control
Computer science
control theory
systems
Control system synthesis
Control theory. Systems
Exact sciences and technology
Exponentially stable
Mathematical methods in physics
Nonlinear systems
Numerical approximation and analysis
Ordinary and partial differential equations, boundary value problems
Physics
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Summary:Within the Liapunov framework, a sufficient condition for exponential stability of ordinary differential equations is proposed. Unlike with classical Liapunov theory, the time derivative of the Liapunov function, taken along solutions of the system, may have positive and negative values. Verification of the conditions of the main theorem may be harder than in the classical case. It is shown that the proposed conditions are useful for the investigation of the exponential stability of fast time-varying systems. This sets the stability study by means of averaging in a Liapunov context. In particular, it is established that exponential stability of the averaged system implies exponential stability of the original fast time-varying system. A comparison of our work with results taken from the literature is included.
ISSN:0005-1098
1873-2836
DOI:10.1016/S0005-1098(99)00012-6