Properties of Composite Laplacian Quadratics and Their Applications in Consensus of Linear Differential Inclusions
Fei Chen, Linying Xiang, Wei Ren · IEEE Transactions on Automatic Control · 2015
This technical note introduces a non-quadratic function that is defined in terms of multiple Laplacian quadratics, called the function of composite Laplacian quadratics. The function is mainly used for control synthesis and analysis of multi-agent systems. Some important properties of the function are studied. In particular, the one-level-set dissipation property is established, and the gradient of the function is derived. The function is further applied to solve the consensus problem of linear differential inclusions (LDIs). Finally, a numerical example is given to verify the validity of the derived results.