Consensus of linear differential inclusions via composite Laplacian quadratics

This work studies the properties of a function that is defined in terms of multiple Laplacian quadratics, called the function of composite Laplacian quadratics. The function is further exploited to design and analyze a control algorithm that solves the consensus problem for multi-agent systems described by linear differential inclusions (LDIs). It is shown that if certain bilinear matrix inequalities (BMIs) hold and the network topology is connected, then consensus can be reached exponentially. Finally, a numerical example is given to verify the validity of the derived results.