Feasibility analysis of the bilinear matrix inequalities with an application to multi-objective nonlinear observer design

Yan Wang, Rajesh Rajamani

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

This paper develops a convex optimization method to analyze the feasibility of a nonconvex bilinear matrix inequality (BMI), which is traditionally treated as a NP hard problem. First, a sufficient condition for the convexity of a quadratic matrix inequality (QMI), which is a more general semidefinite constraint than a BMI, is presented. It will be shown that the satisfaction of sufficient convexity condition implies that the QMI constraint can be transferred into an equivalent linear matrix inequality (LMI) constraint, which can be efficiently solved by well-developed interior-point algorithms. This result constitutes perhaps the first systematic methodology to verify the convexity of QMIs in the literature of semidefinite programming (SDP) in Control. For the BMI problem, a method to derive a convex inner approximation is discussed. The BMI feasibility analysis method is then applied to a nonlinear observer design problem where the estimation error dynamics is transformed into a Lure system with a sector condition constructed from the element-wise bounds on the Jacobian matrix of the nonlinearities. The developed numerical algorithm is used to design a nonlinear observer that satisfies multiple performance criteria simultaneously.

Original languageEnglish (US)
Title of host publication2016 IEEE 55th Conference on Decision and Control, CDC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3252-3257
Number of pages6
ISBN (Electronic)9781509018376
DOIs
StatePublished - Dec 27 2016
Event55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States
Duration: Dec 12 2016Dec 14 2016

Publication series

Name2016 IEEE 55th Conference on Decision and Control, CDC 2016

Other

Other55th IEEE Conference on Decision and Control, CDC 2016
CountryUnited States
CityLas Vegas
Period12/12/1612/14/16

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Wang, Y., & Rajamani, R. (2016). Feasibility analysis of the bilinear matrix inequalities with an application to multi-objective nonlinear observer design. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016 (pp. 3252-3257). [7798758] (2016 IEEE 55th Conference on Decision and Control, CDC 2016). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2016.7798758