Containment Control of Fractional-order Nonlinear Multi-agent Systems with Time Delay

Formation control of multi-agent systems is an extension of its consensus problem, which has been widely used in control science and engineering, system science, information and communication engineering and other disciplines. Compared with using integral-order calculus to describe the change of the state of the object, the fractional-order calculus can represent and reflect the real physical characteristics of the object better. In this paper, containment control problem of fractional-order nonlinear multi-agent systems with time delay is studied. In spite of the difficulties and challenges caused by the operator complex property and system delay in fractional-order calculus, this paper solves the containment control problem by constructing a quadratic Lyapunov function and using matrix analysis theory, graph theory and fractional Razumikhin method. The conditions of linear matrix inequalities for asymptotically containment control are given. Finally, numerical simulation results verify the effectiveness of the proposed control scheme.