Robust Feedback Stability of Networked Multi-agent Negative Imaginary Systems on Undirected Graph

The robust stability for networked multi-agent dynamical systems having strict negative imaginary (SNI) uncertainty is discussed in this article. The undirected graph containing at most one self-loop is used to model communication among network agents. The feasibility of control protocol parameters is investigated further in the paper using a set of constraints on linear matrix inequality (LMI). The disciplined convex optimization programming is used to find the feasible solutions of LMIs. The control protocol parameters in this study are computed in such a way that the uncertain networked multi-agent dynamical system is robustly stabilized against strictly negative imaginary (SNI) uncertainty for multiple network topologies. One illustrative design example is also demonstrated to show the efficiency of synthesis method.