Stability Analysis of Fractional Adaptive High-Gain Controllers for a Class of Linear Systems General case

In this paper we demonstrate that a fractional adaptive controller based on the high gain output feedback stabilizes the class of linear, time-invariant, minimum phase, SISO systems of relative degree one. We generalize the stability theorem of integer controllers to fractional order controllers whose derivative order is a real number between one and two, and introduce a new tuning parameter for the performance behaviour of the controlled plant. A simulation example is given to illustrate the effectiveness of the proposed algorithm