Robust stabilization of interval fractional-order plants with an interval time delay by fractional-order proportional integral derivative controllers

This paper concentrates on presenting a reliable procedure to compute the stabilizing region of fractional-order proportional integral derivative (FOPID) controllers for interval fractional-order plants having an interval time delay. An interval fractional-order plant is defined as a fractional-order transfer function whose denominator and numerator coefficients are all uncertain and lie in specified intervals. Also, an interval time delay points to a delay term whose value varies in a specific interval. The D-decomposition technique and the value set concept are employed to determine the stabilizing region of FOPID controllers. In this study, first, a theorem is presented to compute the boundary of the value sets of systems having interval time day. Then, a lemma is provided for robust stability analysis of the given closed-loop control system. For a convenient use of the paper results, an algorithm is proposed to solve the problem of robustly stabilizing interval fractional-order plants with an interval time delay using FOPID controllers. Finally, four examples are provided to illustrate the proposed procedure. In this paper, a new approach is proposed to obtain the stabilizing region of FOPID controllers for interval fractional-order plants with an interval time delay.image