Stabilizing controller design for nonlinear fractional order systems with time varying delays

To deal with stabilizing of nonlinear affine fractional order systems subject to time varying delays, two methods for finding an appropriate pseudo state feedback controller are discussed. In the first method, using the Mittag-Lefler function, Laplace transform and Gronwall inequality, a linear stabilizing controller is derived, which uses the fractional order of the delayed system and the upper bound of system nonlinear functions. In the second method, at first a sufficient stability condition for the delayed system is given in the form of a simple linear matrix inequality (LMI) which can easily be solved. Then, on the basis of this result, a stabilizing pseudo-state feedback controller is designed in which the controller gain matrix is easily computed by solving an LMI in terms of delay bounds. Simulation results show the effectiveness of the proposed methods.