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IMA Journal of Mathematical Control and Information Advance Access originally published online on September 17, 2008
IMA Journal of Mathematical Control and Information 2008 25(4):409-417; doi:10.1093/imamci/dnn004
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Design for positivity of analytic functions

Ezra Zeheb{dagger}

Department of Electrical Engineering, Techion, Haifa, 32000, Israel and Department of Electronics Engineering, Jerusalem College of Engineering, Jerusalem, Israel

Yuri Dolgin{ddagger}

Department of Electrical Engineering, Techion, Haifa, 32000, Israel

{dagger} Email: zeheb{at}ee.technion.ac.il

{ddagger} Corresponding author. Email: yuri_d{at}tx.technion.ac.il

Received on March 27, 2007; Revision received November 14, 2007. Accepted on January 14, 2008

A large group of control problems can be casted as a problem of design for positivity. A new method is presented for choosing a parameter which ensures the robust positiveness of any real analytic function. The method provides an analytic solution as opposed to numerical sampling techniques. The method is especially useful in design for polynomial positivity due to existence of efficient techniques for solution of systems of polynomial equations and inequalities. Examples are provided, which illustrate the applicability of the proposed method to real-life problems.

Keywords: positivity; robust control; stability.


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