Leader-following consensus control of nabla discrete fractional order multi-agent systems

This paper studies a consensus problem for discrete-time linear nabla fractional order multi-agent systems with Riemann-Liouville difference operator. With the help of the discrete fractional Lyapunov direct method, a state feedback stabilization problem of a discrete-time linear nabla fractional order system is firstly analyzed. Then a distributed consensus control law is proposed for a discrete-time linear nabla fractional order multi-agent system. Some sufficient conditions are presented to guarantee that the leader-following consensus can be achieved by the proposed algorithm. The control gain is determined according to an algebraic Riccati inequality. Finally, simulation results are presented to demonstrate the effectiveness of theoretical analysis.