The asymptotic stability of Caputo fractional order switching systems with only continuous vector field functions

In this paper, a theorem with very weak conditions on vector field functions for asymptotic stability of Caputo fractional order switching systems is proposed. Based on Vainikko’s lemmas, the Caputo fractional derivative of a continuously differentiable and convex Lyapunov function, along trajectories of any Caputo fractional order switching systems with vector field function being only continuous, proves to be continuous and have a very useful estimation. This weakens the smoothness requirement on the vector field functions for fractional stability analysis from differentiability as in existing results to only continuity. Finally, the numerical implementation of a Caputo fractional order switching system with only continuous vector field function illustrates the effectiveness of the proposed theorem.