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Journal of Convex Analysis 19 (2012), No. 4, 1009--1015
Copyright Heldermann Verlag 2012

Piecewise Smooth Lyapunov Function for a Nonlinear Dynamical System

Yan Gao
School of Management, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China

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.

Keywords: Nonlinear dynamical system, stability, region of attraction, Lyapnov functions, nonsmooth analysis, piecewise smooth function.

MSC: 90C30, 65H10

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