Exact Delay Bounds of Second-Order Multi-Agent Systems With Input and Communication Delays: From Algebra and Geometric Perspective

Abstract

This brief studies the delay bounds problem of second-order multi-agent systems with input and communication delays under the directed graph. Firstly, the systems with input delay only are studied and the delay margin of input delay is given. Then the critical value of communication delay is considered for the fixed input delay within the proposed scope. Then, the input delay and communication delay are analyzed simultaneously from geometric perspective. The explicit geometric description of the consensus crossing curves is obtained. Then the consensus regions can be completely determined.