Pseudo state feedback stabilization of commensurate fractional order systems

This paper addresses the problem of pseudo state feedback stabilization of commensurate fractional order systems. In the proposed approach, Linear Matrix Inequalities (LMI) formalism is used to check if the pseudo state matrix eigenvalues belong to the non convex fractional system stability region of the complex plane. A new LMI stability condition is first proposed. Based on this condition, a necessary and sufficient LMI method for the design of stabilizing controllers is given. Its efficiency is evaluated on an inverted fractional pendulum stabilization problem.