Asymptotic stability of distributed order nonlinear dynamical systems

In this article we present a generalization of the Lyapunov direct method for distributed order nonlinear time-varying systems. By extending recently introduced properties of the Caputo fractional derivative to the distributed order case, we provide various ways to determine the stability or asymptotic stability of certain systems. The fractional results that inspired this work are recovered if an appropriate distribution function is chosen. Some examples are given to validate the obtained results.