This book explores admissible consensus analysis and design problems concerning singular multi-agent systems, addressing various impact factors including time delays, external disturbances, switching topologies, protocol states, topology structures, and performance constraint. It also discusses the state-space decomposition method, a key technique that can decompose the motions of singular multi-agent systems into two parts: the relative motion and the whole motion. The relative motion is independent of the whole motion. Further, it describes the admissible consensus analysis and determination of the design criteria for different impact factors using the Lyapunov method, the linear matrix inequality tool, and the generalized Riccati equation method. This book is a valuable reference resource for graduate students of control theory and engineering and researchers in the field of multi-agent systems.