Variable structure control of fractional time-delay systems

In this paper, a variable structure control design is presented for a class of fractional time-delay systems of incommensurate order. First, a stable switching manifold, independent of the delay, is designed for a virtual integer-order system. Then, a switched controller that guarantees convergence to the sliding surface is developed. The premise of the design methodology is based on the fact that the stability region of the integer system is a subset of the stability region of the corresponding fractional-order system. An illustrative example is given to illustrate the main idea of this work.