On the positivity of multivariable scalar functions

The determination of local and global positivity (or negativity) of general nonlinear functions plays a fundamental role in several applied mathematic al areas. In this work, this subject is addressed by the presentation of a new theorem that allows to determine the sign of a function and furnishes a n estimate of the local region maintaining this sign. Applications to Lyapu nov stability theory and nonlinear H-infinity control are presented as exam ples of the applicability of the theorem. (C) 2001 The Franklin institute. Published by Elsevier Science Ltd. All rights reserved.