Robust fractional controller for interval first order system with time delay

In this paper, a new method is proposed to define the parameters of fractional order PIλ controller that stabilise an uncertain first order system with time delay. In fact, based on an extension version of Hermite-Biehler theorem and Pontryagin theorem the complete set stabilising PIλ parameters (KP, Ki, λ) is determined. The closed-loop characteristic equation of the system is a fractional order quasi-polynomial with interval uncertainty structure which is decomposed into several vertex. In the complex plane the value set of the vertex is a convex polygon. Simulation results are given to show the effectiveness of the proposed method.