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Social interactions influence our thoughts, opinions and actions. In thispaper, social interactions are studied within a group of individuals composedof influential social leaders and followers. Each person is assumed to maintaina social state, which can be an emotional state or an opinion. Followers updatetheir social states based on the states of local neighbors, while socialleaders maintain a constant desired state. Social interactions are modeled as ageneral directed graph where each directed edge represents an influence fromone person to another. Motivated by the non-local property of fractional-ordersystems, the social response of individuals in the network are modeled byfractional-order dynamics whose states depend on influences from localneighbors and past experiences. A decentralized influence method is thendeveloped to maintain existing social influence between individuals (i.e.,without isolating peers in the group) and to influence the social group to acommon desired state (i.e., within a convex hull spanned by social leaders).Mittag-Leffler stability methods are used to prove asymptotic stability of thenetworked fractional-order system.

Containment Control for a Social Network with State-Dependent Connectivity