Leader-following consensus for singular swarm systems

Admissible leader-following consensus problems for high-order linear singular swarm systems are investigated. Firstly, by decomposing the dynamic of each agent into two parts with model transformation, admissible leader-following consensus problems are converted into admissible problems of multiple singular subsystems, and a necessary and sufficient condition is obtained by solving the state response of the singular swarm system. Then, a sufficient condition for admissible leader-following consensualizability is given, and based on the algebraic Riccati equation, an approach to determine gain matrices in consensus protocol is presented. Finally, a numerical example is given to demonstrate the effectiveness of theoretical results.