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 mathematical 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 an estimate of the local region maintaining this sign. Applications to Lyapunov stability theory and nonlinear H-infinity control are presented as examples of the applicability of the theorem.