Robust Stabilization of Networked Multi-agent Systems with Strict Negative Imaginary Uncertainties: An LMI Approach
Ola Skeik, Alexander Lanzon · 2018
This paper presents sufficient conditions, in a linear matrix inequality (LMI) framework, for a control protocol to robustly stabilize a networked multi-agent system in the presence of strict negative imaginary (SNI) uncertainties with certain DC size. The control protocol under consideration is based on relative state measurements of neighbouring agents and absolute state measurements of a subset of agents and therefore the network graph which models the information exchange among agents is assumed a connected undirected graph with at least one self-loop. Under such assumptions on the network graph it is shown that the negative imaginary (NI) property of the networked system is unchanged due to transformation. Hence, the sufficient conditions are derived based on multiple reduced order subsystems satisfying the NI property simultaneously. The paper also summarizes the steps required to design the control protocol parameters; which are a positive scalar and a gain matrix. It is shown that appropriately adjusting the positive scalar while leaving the gain matrix unchanged guarantees robustness of the control protocol to variations in the network topology as well as robustness to SNI uncertainties. A numerical example is given to show the usefulness of the proposed results.