Robust stabilization of fractional order interval systems via a fractional-order PID controller

This paper presents a solution to the problem of stabilizing a fractional order interval system (FOIS) by fractional order PID control. On the basis of the Extended Kharitonov Theorem, the problem of testing robust stability of a fractional order interval polynomial is transformed into one of checking stability of a family of vertex sub-polynomials whose value set is represented by a convex parpolygon with the same number of vertices. The stability region of each vertex sub-polynomial is then obtained by using the D-partition method. Consequently, the robust stabilization region of an FOIS via a fractional order PID controller is determined as the intersection of the stability regions of these vertex sub-polynomials. Numerical examples are used to illustrate the effectiveness of the proposed method.