Necessary and Sufficient Conditions for Extended Strictly Positive Realness of Singular Fractional-Order Systems

The extended strictly positive realness of singular fractional-order systems with the fractional-order α ∈ (1,2) is investigated in this brief. Firstly, a novel sufficient and necessary condition for the extended strictly positive realness of fractional-order systems is derived in terms of linear matrix inequalities. Secondly, a novel sufficient and necessary condition for the admissibility and extended strictly positive realness of singular fractional-order systems is obtained in terms of linear matrix inequalities with equality constraints. Finally, two examples are presented to show the effectiveness of the obtained methods.