Due to the world's aging population, the development of affordable and easy to use wheelchairs is becoming a priority. In this study, the control of an automated wheelchair is proposed. The model equations are derived from the Euler-Lagrange equations, then a descriptor model is formulated. Next, a Takagi-Sugeno descriptor model with a limited number of rules is derived. The control and observation of the model is studied using the delayed non-quadratic Lyapunov function. The closed loop stability is proven using the separation theorem. Lastly, simulation results are given and discussed.