Stabilizing and Robust Fractional PID Controller Synthesis for Uncertain First-Order plus Time-Delay Systems

Algorithm 3

Stability of uncertain time-delay system.

(1)	Define by equation (19).
(2)	Produce exposed edges by equation (20).
(3)	Compose the set of exposed edges, , equation (21).
(4)	Using Algorithm 1, the allowable ranges of of each vertex (19) is found.
(5)	Determine the intersection of all the intervals.
(6)	Using Algorithm 2, we compute the () stabilizing values for the entire family.
(7)	Plot the robust stability region for every vertex in the plan.