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