LMI approach of H∞ consensus for multi-agent systems under Markov switching topology by dynamic output-feedback controller

This study investigates the $H_{\infty }$ consensus problem for multi-agent systems under Markov switching topology by designing a dynamic output-feedback (DOF) controller. First, an invariant property is presented to address the Markov switching topology utilizing the eigenvalues and eigenvectors of the Laplacian matrix. Second, the eigenvalues of each Laplacian matrix are regarded as bounded uncertainties, representing the variations between the second smallest eigenvalue and the largest eigenvalue, removing the effect of variable eigenvalues. Using the elimination lemma, the equivalent consensus conditions are derived as Linear Matrix Inequalities (LMIs) for the cases both without and with external disturbances. Finally, the DOF controller for $H_{\infty }$ consensus is designed by solving the LMIs. Numerical examples are provided to verify the validity of the main results.