Geodesic
New qualitative methods for stability of delay systems
Kybernetika, Tome 37 (2001) no. 3, p. [229]

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A qualitative method is explored for analyzing the stability of systems. The approach is a generalization of the celebrated Lyapunov method. Whereas classically, the Lyapunov method is based on the simple comparison theorem, deriving suitable candidate Lyapunov functions remains mostly an art. As a result, in the realm of delay equations, such Lyapunov methods can be quite conservative. The generalization is here in using the comparison theorem directly with a different scalar equation with known qualitative behavior. It leads to criteria for stability of general difference and delay differential equations.
Classification : 34K20, 93C23, 93D05, 93D30
Keywords: stability of systems; delay system; Lyapunov method 
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     author = {Verriest, Erik I.},
     title = {New qualitative methods for stability of delay systems},
     journal = {Kybernetika},
     pages = {[229]},
     publisher = {mathdoc},
     volume = {37},
     number = {3},
     year = {2001},
     mrnumber = {1859082},
     zbl = {1265.93191},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2001__37_3_a1/}
}
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Verriest, Erik I. New qualitative methods for stability of delay systems. Kybernetika, Tome 37 (2001) no. 3, p. [229]. http://geodesic.mathdoc.fr/item/KYB_2001__37_3_a1/