𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the positivity of multivariable scalar functions

✍ Scribed by Luı́s Gustavo Soares Longhi; Argimiro Resende Secchi; Enrique Luis Lima

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
120 KB
Volume
338
Category
Article
ISSN
0016-0032

No coin nor oath required. For personal study only.

✦ Synopsis

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.

📜 SIMILAR VOLUMES

Ladder realizations of multivariable pos
Ladder realizations of multivariable positive real functions
✍ M.O. Ahmad; C.H. Reddy; V. Ramachandran; M.N.S. Swamy 📂 Article 📅 1979 🏛 Elsevier Science 🌐 English ⚖ 683 KB

Necessary and sufficient conditions are obtained for the realization of an m-variable positive real function (PRF) as the impedance function of a resistivelyterminated ladder network of m lossless two-ports connected in cascade. Each two-port is a single-variable lossless ladder with all of ifs tran

On the positivity of symmetric polynomia
On the positivity of symmetric polynomial functions.: Part I: General results
✍ Vlad Timofte 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 177 KB

We prove that a real symmetric polynomial inequality of degree d 2 holds on R n + if and only if it holds for elements with at most d/2 distinct non-zero components, which may have multiplicities. We establish this result by solving a Cauchy problem for ordinary differential equations involving the

Some Theorems on sum Separability of Mul
Some Theorems on sum Separability of Multivariable Reactance and Positive Real Functions
✍ V. Ramachandran; C.H. Reddy; M.N.S. Swamy 📂 Article 📅 1977 🏛 Elsevier Science 🌐 English ⚖ 463 KB

New necessary and sufficient conditions, which are also algorithmic in nature, are obtained for the decomposition of a multivariable reactance function or a multivariable positive real function into a sum of several single variable reactance functions or several single variable positive real functio