Asymptotically exact H2 guaranteed cost computation by means of a special parameter-dependent Lyapunov function

This paper deals with guaranteed, H₂ norm computation for continuous-time uncertain linear systems in convex bounded domains. As main result, we show that a special choice for the parameter-dependent Gramian solution allows us to establish a convergent sequence of polynomially parameter-dependent linear matrix inequalities whose solutions are constant symmetric matrices parametrized in terms of an integer k. Then, we propose some linear matrix inequality relaxations to numerically compute the H₂ guaranteed cost and we investigate the trade off between accuracy of the results and computational effort.