Semi-global leader-following output consensus for heterogeneous fractional-order multi-agent systems with input saturation via observer-based protocol

Abstract

In this paper, semi-global leader-following output consensus problem for heterogeneous fractional-order multi-agent systems with input saturation and external disturbances is investigated. The case where the dynamics are integer-order can be viewed as a special case of fractional-order systems. First, a novel observer-based consensus algorithm is designed to solve the semi-global output consensus problem. It is worth noting that the consensus is semi-global since the set of initial states is bounded. Then, the low gain feedback technique is utilized based on the solution of a parametric algebraic Riccati equation. Moreover, sufficient conditions of output consensus for heterogeneous fractional-order multi-agent systems are derived by using algebraic graph theory, matrix theory and the stability theory of fractional-order systems. It can be proven that the output signals of followers can reach synchronization with the leader’s. Finally, numerical examples are provided to illustrate the effectiveness of our conclusions.