Uncertain system analysis: an LMI approach with applications

We investigate the performance analysis of uncertain systems. As it was initially proposed by Zames (1981), performance of an uncertain system is measured by estimating the set of output signals corresponding to a given set of input signals. Sets of signals are described by quadratic constraints. Based on a topological framework, we first propose necessary and sufficient conditions for robust performance, which are relaxed to sufficient but convex ones. We then focus on the practical performance estimation. All the proposed conditions leads to convex optimization problems involving linear matrix inequality constraints.