Robust Discrete-time Consensus of Multi-agent Systems with Uncertain Interaction

This paper addresses robust discrete-time consensus problem of multiple agents with uncertain structure, where the network coupling weights are supposed polynomial functions of an uncertain vector constrained in a semialgebraic set. Based on the Lyapunov stability theory, a necessary and sufficient condition for robust discrete-time consensus is proposed. Then, we investigate the robust discrete-time consensus with positive weighted network, and a necessary and sufficient condition is also provided based on the property of an uncertain matrix. Corresponding sufficient conditions for robust discrete-time consensus are derived by solving a linear matrix inequality (LMI) problem built by exploiting sum-of-squares (SOS) polynomials. Some examples illustrate the proposed results.