Optimal Static Output Feedback Stabilization of Fractional-Order Systems With Caputo Derivative Order 1 ≤ α < 2

The design of optimal static output feedback controllers for fractional-order linear systems with Caputo derivative order 1 ≤ α < 2 is addressed in this paper. The cost function to be minimized is the Frobenius norm of the feedback matrix. First, based on the barrier method, we demonstrate how to create an auxiliary minimization problem that is easier to solve than the original optimization problem. The auxiliary problem is then solved numerically to obtain an approximate solution to the original problem. Necessary conditions for the optimal solution of the auxiliary minimization problem are derived using the Lagrange multiplier method. A numerical example is provided to validate the proposed method.