Adaptive sliding mode control for a class of Caputo type fractional-order interval systems with perturbation

This study is concerned with the stabilisation problem for a class of Caputo type fractional-order interval systems with perturbation. Employing Riemann-Liouville fractional integral sliding surface, a novel robust sliding mode control law is established to drive the dynamics of the system to the manifold s=0 in finite time. Based on linear matrix inequality criterions and stability theorems, the closed-loop system will asymptotically converge to the origin as time progresses. Meanwhile, the unknown perturbation is well adjusted on-line by the designed adaptive law. Furthermore, a new reaching law is introduced to reduce the chattering which is caused by the discontinuity of the switching function, and to improve the robustness and the stability of system. Besides, some results about the control and stabilisation of fractional-order interval systems are illustrated in this study; several comparisons with the related works are given to reveal the potential advantages of the proposed controller over the previous results. Finally, an example with numerical simulations is provided to show the validity and feasibility of the proposed method.