Synchronization-based Estimation of the Maximal Lyapunov Exponent of Nonsmooth Systems

Abstract

The maximal Lyapunov exponent of a nonsmooth system is the lower bound for the proportional feedback gain necessary to achieve full state synchronization. In this paper, we prove this statement for the general class of nonsmooth systems in the framework of measure differential inclusions. The results are used to estimate the maximal Lyapunov exponent using chaos synchronization, which is illustrated on an impact oscillator.