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On the positivity of multivariable scalar functions

Authors
Journal
Journal of the Franklin Institute
0016-0032
Publisher
Elsevier
Publication Date
Volume
338
Issue
4
Identifiers
DOI: 10.1016/s0016-0032(00)00086-7
Keywords
  • Nonlinear Systems
  • Control Theory
  • Nonlinear Quadratic Forms
  • Positivity
Disciplines
  • Mathematics

Abstract

Abstract 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.

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