Algebraic criteria for consensus problems of general linear multi-agent systems with switching topology

This paper considers leaderless consensus problem and leader-following consensus problem for general linear multi-agent systems with switching interaction topology. Based on the relative states of the neighboring agents, two distributed control protocols are presented. By investigating the null space of a group of Riccati equations, algebraic criteria for the consensus problems are established, and further discussions on the preconditions of the theorems are proposed. Numerical simulations on multi-agent systems are presented to demonstrate the efficiency of our criteria.