Synchronization via output feedback for multi-agent singularly perturbed systems with guaranteed cost
A set of \(n\) identical singularly perturbed linear control systems (called agents) is considered. It is assumed that each agent has access to relative measurements for the output of some neighbors. The interaction structure is captured by an undirected connected graph and an unknown weighted adjacency matrix. It is assumed that the eigenvalues of the corresponding weighted Laplacian matrix are uncertain but belong to known compact intervals. The problem is to design an output feedback consensus protocol that ensures the synchronization of all agents with a global guaranteed cost. This problem is reduced to the problem of dynamic output feedback robust stabilization of a singularly perturbed uncertain linear system with guaranteed cost. Sufficient conditions for solving these problems (expressed in terms of linear matrix inequalities concerning the slow and fast dynamics) are presented. The proposed approach allows handling nonstandard singularly perturbed systems, where the fast dynamic matrix can be singular or unstable. Three illustrative examples show the applicability of the obtained results.
scientific article; zbMATH DE number 7338074