Leader-following consensus conditions for fractional-order descriptor uncertain multi-agent systems with 0 < α < 2 via output feedback control

The leader-following consensus problem for fractional-order uncertain multi-agent systems with descriptor linear dynamics is investigated in this paper. Firstly, a consensus protocol is proposed based on output feedback when fractional-order α satisfies 0 < α < 2. Secondly, an appropriate transformation is conducted to transform consensus problem into stability problem. Based on stability theory of fractional-order systems, sufficient conditions are presented to guarantee the leader-following consensus of fractional-order descriptor uncertain multi-agent systems with 0 < α < 2. In addition, output feedback controller is designed by using linear matrix inequality approach and matrix's singular value decomposition. Finally, numerical examples are given to illustrate the effectiveness of our conclusions.