INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL Int. J. Robust. Nonlinear Control 2010; 00:1–19 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/rnc Robust Consensus for Uncertain Multi-Agent Systems with Discrete-Ti

This paper investigates robust consensus for multi-agent systems with discrete-time dynamics affected by uncertainty. In particular, the paper considers multi-agent systems with single and double integrators, where the weighted adjacency matrix is a polynomial function of uncertain parameters constrained into a semialgebraic set. Firstly, necessary and sufficient conditions are provided for robust consensus based on the existence of a Lyapunov function polynomially dependent on the uncertainty. In particular, an upper bound on the degree required for achieving necessity is provided. Secondly, a necessary and sufficient condition is provided for robust consensus with single integrator and nonnegative weighted adjacency matrices based on the zeros of a polynomial. Lastly, it is shown how these conditions can be investigated through convex programming by exploiting linear matrix inequalities and sums of squares of polynomials. Some numerical examples illustrate the proposed results. Copyright c © 2010 John Wiley & Sons, Ltd