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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
##### Keywords:
linear fast periodic systems
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