Bounded Real Lemmas for Singular Fractional-Order Systems: The 1 < α < 2 Case

Abstract

This brief investigates the problems of bounded real lemmas in the sense of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> norm for singular fractional-order systems with the commensurate order 1 <; α <; 2. Firstly, novel necessary and sufficient conditions for the bounded real lemmas in the sense of H norm for singular fractional-order systems are proposed in the form of linear matrix inequalities with equality constraints. Secondly, for singular fractional-order systems with norm bounded uncertainties, the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller synthesis problem is analyzed and the corresponding H controller is designed based on the bounded real lemmas. Finally, an illustrative example about the singular fractional-order electrical circuit is given to show the effectiveness of the obtained bounded real lemmas.