New LMI conditions for stability and stabilizability of fractional-order systems with H∞ performance

New extended Linear Matrix Inequality (LMI) conditions for H-infinity control analysis and synthesis of fractionalorder systems of commensurate type are developed. The first condition is mainly devoted to fractional-order systems with non-integer-differentiation order alpha is an element of [1, 2[ while the second LMI condition concerns the case where the differentiation order alpha is an element of]0, 1[. For each independent case, the newly developed condition appears as a unique inequality that ensures the stability of the system with a H-infinity bound parameterized as an LMI variable. The proposed LMI conditions are found quite useful for H-infinity control with static state feedbacks and staticoutput feedbacks as well.