Abstract
This chapter investigates the gap between positive forms and SOS forms. Conservatism of the LMI relaxations described in Chapter 1 is related to the existence of positive forms which are not SOS, called PNS forms. a priori conditions for non-conservatism of these relaxations are presented for some classes of forms. The class of SMR-tight forms is introduced in order to derive a posteriori tightness conditions. A further contribution of this chapter consists of providing a parametrization of the set of PNS forms. It is shown that the set of PNS forms is dense in the space of forms, that each PNS form is the vertex of a cone of PNS forms, and how PNS forms can be constructed via the SMR.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2009 Springer London
About this chapter
Cite this chapter
Chesi, G., Garulli, A., Tesi, A., Vicino, A. (2009). Positivity Gap. In: Homogeneous Polynomial Forms for Robustness Analysis of Uncertain Systems. Lecture Notes in Control and Information Sciences, vol 390. Springer, London. https://doi.org/10.1007/978-1-84882-781-3_2
Download citation
DOI: https://doi.org/10.1007/978-1-84882-781-3_2
Publisher Name: Springer, London
Print ISBN: 978-1-84882-780-6
Online ISBN: 978-1-84882-781-3
eBook Packages: EngineeringEngineering (R0)