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Stability of fast periodic systems. (English) Zbl 0557.93055
The stability of linear fast periodic systems \(x'=(A+\frac{1}{\epsilon}B(\frac{t}{\epsilon}))x\) is analyzed for small \(\epsilon >0\) by the eigenvalues of \[ \lim_{T\to \infty}\frac{1}{T}\int^{T}_{0}\phi^{-1}(s,0)A\phi (s,0)ds, \] where B(t) is periodic with zero average and \(\phi\) (t,0) is the fundamental matrix of \(x'=B(t)x\).
Reviewer: J.Kato

MSC:
93D20 Asymptotic stability in control theory
34C25 Periodic solutions to ordinary differential equations
93C05 Linear systems in control theory
15A18 Eigenvalues, singular values, and eigenvectors
93C99 Model systems in control theory
34D05 Asymptotic properties of solutions to ordinary differential equations
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