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.

研究了带有描述符线性动力学的分数阶不确定多主体系统的前导跟随共识问题。首先，基于分数阶α满足0 <  α  <2时的输出反馈，提出了一种共识协议。其次，进行了适当的变换，将共识问题转化为稳定性问题。基于分数阶系统的稳定性理论，给出了充分的条件来保证分数阶描述符不确定的不确定多主体系统在0 < α时的前导跟随共识  <2.另外，通过使用线性矩阵不等式方法和矩阵的奇异值分解来设计输出反馈控制器。最后，通过数值例子说明了我们结论的有效性。