Adaptive control for discontinuous variable-order fractional systems with disturbances

This paper deals with the global asymptotic stabilization and finite-time stabilization issues for variable-order fractional systems with partial a priori bounded disturbances by designing an appropriate adaptive controller. Via the inductive method and Arzela-Ascoli theorem, the existence and uniqueness of the solution for the considered system is firstly verified under the proposed control strategy. By applying Lyapunov stability theory, non-smooth analysis and inequality technique, sufficient stabilization criteria are established under the framework of variable-order fractional Filippov differential inclusion. Finally, two numerical simulations are given to demonstrate the validity of the proposed method.

Automated summary

This paper addresses the issues of global asymptotic stabilization and finite-time stabilization for variable-order fractional systems with partial a priori bounded disturbances by designing an appropriate adaptive controller. The existence and uniqueness of the solution for the considered system under the proposed control strategy is verified using the inductive method and Arzela-Ascoli theorem. Sufficient stabilization criteria are established under the framework of variable-order fractional Filippov differential inclusion through Lyapunov stability theory, non-smooth analysis, and inequality technique.