Lyapunov Exponents for Systems Described by Differential Equations with Discontinuous Right-Hand Sides

This paper discusses the numerical computation of Lyapunov exponents for systems described by ordinary differntial equations with discontinuous right-hand sides. Known methods for computing Lyapunov exponents we extended to such systems by using jump conditions for the variational equation and treating sliding behavior explicitly. A computer program that computes Lyapunov exponents for linear plants cotrolled by bang-bang control according to a linear switching law is briefly described. Examples include one involving the stabilization of the longitudinal dynamics of a helicopter.