Geodesic
Asymptotic Behavior in Sliding Mode Control Systems
Serdica Mathematical Journal, Tome 39 (2013) no. 3-4, pp. 215-232.

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Practical stability of real states of nonlinear sliding mode control systems is related to asymptotic vanishing of the corresponding sliding errors. Conditions are found such that, if the equivalent control achieves exponential stability, then real states are practically stable. In special cases, their exponential stability is obtained. A link between convergence of regularization procedures and metric regularity is pointed out. 2010 Mathematics Subject Classification: 93B12, 93D15.
Keywords: sliding mode control, practical stability, asymptotic convergence 
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     title = {Asymptotic {Behavior} in {Sliding} {Mode} {Control} {Systems}},
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Zolezzi, Tullio. Asymptotic Behavior in Sliding Mode Control Systems. Serdica Mathematical Journal, Tome 39 (2013) no. 3-4, pp. 215-232. http://geodesic.mathdoc.fr/item/SMJ2_2013_39_3-4_a3/