Synchronization-based estimation of the maximal Lyapunov exponent of nonsmooth systems (INVITED)

Abstract eng:
Lyapunov exponents of chaotic attractors are hard to estimate, especially for non-smooth systems. One method to estimate the maximal Lyapunov exponent is by using its relationship with the synchronization properties of coupled systems. The maximal Lyapunov exponent is equal to the minimal proportional feedback gain necessary to achieve filll state synchronization with a replica system. In this paper, we prove this statement for the general class of nonsmooth systems in the framework of measure differential inclusions. Numerical results of a mechanical impact oscillator illustrate the effectiveness of the method for nonsmooth systems.

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