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Semi-global practical asymptotic stability and averaging

✍ Scribed by Andrew R. Teel; Joan Peuteman; Dirk Aeyels

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
109 KB
Volume
37
Category
Article
ISSN
0167-6911

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✦ Synopsis

We prove a generalized Liapunov theorem which guarantees practical asymptotic stability. Based on this theorem, we show that if the averaged system αΊ‹ = fav(x) corresponding to αΊ‹ = f(x; t) is globally asymptotically stable then, starting from an arbitrarily large set of initial conditions, the trajectories of αΊ‹ = f(x; t= ) converge uniformly to an arbitrarily small residual set around the origin when ΒΏ 0 is taken su ciently small. In other words, the origin is semi-globally practically asymptotically stable.

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The global asymptotic stability of "second-order" relay control systems with negative eigenvalues is shown to be a consequence of the nonexistence of symmetric periodic solutions. The result shows further that, ezcept for a special case, the solutions reach tke origin in fkwitc time.