Robust consensus of fractional-order singular uncertain multi-agent systems

This paper focuses on consensus analysis of fractional-order singular multi-agent systems (FOSMASs) with uncertainties under fixed topology. The definition of admissible consensus or robust admissible consensus of FOSMASs is proposed and the communication network topology is assumed to be an undirected or a directed graph. Through a coordinate transformation, the admissible consensus of FOSMASs is converted into two parts, one is regularity and impulse-free of single fractional-order singular (FOS) linear system, another one is admissibility of multiple FOS linear systems. The consensus conditions are expressed by linear matrix inequalities (LMIs) via SVD technique. Some simulation examples are given to show how to solve LMIs to get the control gain. The simulation results display that the states of the FOSMAS can achieve consensus by using the solved control gain.