Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Yan Gao

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

gaoyan@usst.edu.cn

Keywords

  • Nonlinear dynamical system
  • stability
  • region of attraction
  • Lyapnov functions
  • nonsmooth analysis
  • piecewise smooth function

Mathematics Subject Classification

90C30, 65H10

Suggested citation

Y. Gao. “Piecewise Smooth Lyapunov Function for a Nonlinear Dynamical System.” Journal of Convex Analysis 19 (2012), No. 4, 1009–1015.

Copyright Heldermann Verlag 2012