This work is concerned with consensus control for a class of leader-following multi-agent systems (MASs). The information that each agent received is corrupted by measurement noises. To reduce the impact of noises on consensus, time-varying consensus gains are adopted, based on which consensus protocols are designed. By using the tools of stochastic analysis and algebraic graph theory, a sufficient condition is obtained for the protocol to ensure strong mean square consensus under the fixed topologies. This condition is shown to be necessary and sufficient in the noise-free case. Furthermore, by using a common Lyapunov function, the result is extended to the switching topology case.

This paper is focused on formability of multi-agent systems (MASs). The problem is concerned with the existence of a protocol that has the ability to drive the MAS involved to the desired formation, and thus, is of essential importance in designing formation protocols. Formability of an MAS depends on several key factors: agents' dynamic structures, connectivity topology, properties of the desired formation and the admissible control set. Agents of the MASs considered here are described by a general continuous linear time-invariant (LTI) model. By using the matrix analysis and algebraic graph theory, some necessary and sufficient conditions on formability of LTI-MASs are obtained. These conditions characterize in some sense the relationship of formability, connectivity topology, formation properties and agent dynamics with respect to some typical and widely used admissible protocol sets.

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