Containment Control of Fractional-Order Multi-Agent Systems with Different Fractional Orders

The current work deals with the containment control problem for a fractional-order multi-agent system containing different fractional orders. To solve this problem, some conditions are extracted to guarantee the asymptotic stability of a particular case of multi-order fractional systems. These conditions are obtained in terms of fractional-orders and the state-space matrix. Then, a multi-agent system containing fractional-order integrator agents with different orders is considered. Now, under a fixed undirected topology, sufficient conditions are extracted to realize the convergence of the agent positions to the convex hull constructed by the virtual leaders. A numerical example is presented to evaluate the accuracy of the presented distributed containment control protocol.