Infinite horizon state-feedback LQR controller for fractional systems

In this paper two versions of the LQR algorithm for fractional order state-space system are presented. For the case of infinite time horizon, and under assumptions of being in the middle of the control process the algorithm has the same form as for integer order case. A new tuning parameter is introduced to modify the algorithm assuming different moments of the control process. Numerical examples are included to present the validity of the proposed solutions.