Geodesic
Piecewise Smooth Lyapunov Function for a Nonlinear Dynamical System
Journal of convex analysis, Tome 19 (2012) no. 4, pp. 1009-1015.

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We study stability and attraction for a nonlinear dynamical system with nonsmooth Lyapunov functions. The previous results on stability and attraction with a max-type Lyapunov function are extended to the case where Lyapunov function is piecewise smooth. A condition, under which stability and attraction are guaranteed with a piecewise smooth Lyapunov function, is proposed. Taking two certain classes of piecewise smooth functions as Lyapunov functions, related conditions for stability and attraction are developed.
Classification : 90C30, 65H10
Mots-clés : Nonlinear dynamical system, stability, region of attraction, Lyapnov functions, nonsmooth analysis, piecewise smooth function 
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     author = {Y. Gao},
     title = {Piecewise {Smooth} {Lyapunov} {Function} for a {Nonlinear} {Dynamical} {System}},
     journal = {Journal of convex analysis},
     pages = {1009--1015},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2012},
     url = {http://geodesic.mathdoc.fr/item/JCA_2012_19_4_JCA_2012_19_4_a6/}
}
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Y. Gao. Piecewise Smooth Lyapunov Function for a Nonlinear Dynamical System. Journal of convex analysis, Tome 19 (2012) no. 4, pp. 1009-1015. http://geodesic.mathdoc.fr/item/JCA_2012_19_4_JCA_2012_19_4_a6/