Abstract
This brief studies local and global synchronization in multiagent systems with nonlinear dynamics with respect to equilibrium points and periodic orbits. For local synchronization, a method is proposed based on the transformation of the original system into an uncertain polytopic system and on the use of homogeneous polynomial Lyapunov functions. For global synchronization, another method is proposed based on the search for a suitable polynomial Lyapunov function. The proposed methods exploit linear matrix inequalities and have several advantages. In particular, the proposed methods require the solution of convex optimization problems. Also, the proposed methods exploit more complex Lyapunov functions than the quadratic Lyapunov functions typically considered in the literature and included in this brief as a special case.
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