Generalized multi-synchronization: A leader-following consensus problem of multi-agent systems

In this paper, the problem of Generalized Multi-Synchronization (GMS) in master-slave topology is addressed. Within a differential algebraic framework this problem is interpreted as a leader-following consensus problem of Multi-Agent Systems (MAS). Here, a multi-agent system is treated as a network of interconnected systems with strictly different dynamics of same dimension, fixed and not strongly connected topology. Multi-agent system is carried out to a Multi-output Generalized observability Canonical Form (MGOCF) with a family of transformations obtained from an adequate selection of the differential primitive element as a linear combination of state measurements and control inputs. This allow us to explicitly give the synchronization algebraic manifold and design a dynamic consensus protocol able to asymptotically achieve consensus for all agents in the network. Finally a worked out example is provided to illustrate the methodology proposed.