Parameter-dependent Slack variable approach for positivity check of polynomials over hyper-rectangle

Authors:
Masayuki Sato
Affiliations:
Institute of Space Technology and Aeronautics, Japan Aerospace Exploration Agency, Mitaka, Tokyo, Japan
Venue:
ACC'09 Proceedings of the 2009 conference on American Control Conference
Year:
2009

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Abstract

This paper addresses the positivity check of polynomials in which the region of indeterminates is given as a hyper-rectangle. A new tractable quadratically parameter-dependent condition is proposed using Parameter-Dependent Slack Variables (PDSVs) which are up to second-order with respect to the indeterminates. It is proved that our derived condition always holds if the condition via Sum-Of-Squares (SOS) approach holds. In addition, as the polynomials defining the region of the indeterminates always satisfy constraint qualification, our proposed method is proved to be a sufficient condition which asymptotically becomes a necessary and sufficient condition for our addressed problem with increase of the sizes of PDSVs.