Fuzzy fractional sliding mode observer design for a class of nonlinear dynamics of the cancer disease

The purpose of this paper is designing to optimise controller parameters for improvement of the performances of cancer dynamic by combining both TS fuzzy sliding mode method and fractional variable structure control. The fractional fuzzy controller matched is formulated here. This paper is proven the stability conditions based on linear matrix inequalities (LMIs) where the fractional-order α belongs to 0 < α < 1. Furthermore, this method is investigated TS fuzzy method to design fractional observer to estimate states of the fractional nonlinear dynamic of drug administration in cancer chemotherapy based on the sector nonlinearity method. This approach presented a mathematical model to expand the dynamics between tumour cells, normal cells, immune cells, chemotherapy drug concentration and drug toxicity. The stability of the closed loop system and the convergence of both the observer and the tracking error to zero are the main merits of the proposed method. The simulation results show the promising perform...