A linear matrix inequality approach to compute H (infinity) guaranteed costs by means of parameter-dependent Lyapunov functions is presented in this paper. The uncertain linear time-invariant systems are supposed to belong to convex bounded domains (polytope-type uncertainty). The conditions proposed are less conservative than other parameter-dependent based method!; from the literature, providing better estimates of worst-case H-infinity norms, in both continuous-and discrete-time systems, as illustrated by means of numerical examples. (C) 2004 Elsevier Ltd. All rights reserved.