LMI relaxations for robust H2 performance analysis of polytopic linear systems

This paper investigates the evaluation of H₂ guaranteed costs of linear uncertain systems in polytopic domains by means of a particular type of polynomial parameter-dependent Lyapunov function. This class of functions, which depend on the dynamic matrix of the system, has been recently proposed for robust stability analysis and is extended here to cope with H₂ guaranteed costs, providing an alternative LMI relaxation which presents a good trade-off between computational burden and accurate results. The results are illustrated by several numerical examples