NDLI: LMI Techniques for Optimization Over Polynomials in Control: A Survey

Content Provider	IEEE Xplore Digital Library
Author	Chesi, G.
Copyright Year	1963
Abstract	Numerous tasks in control systems involve optimization problems over polynomials, and unfortunately these problems are in general nonconvex. In order to cope with this difficulty, linear matrix inequality (LMI) techniques have been introduced because they allow one to obtain bounds to the sought solution by solving convex optimization problems and because the conservatism of these bounds can be decreased in general by suitably increasing the size of the problems. This survey aims to provide the reader with a significant overview of the LMI techniques that are used in control systems for tackling optimization problems over polynomials, describing approaches such as decomposition in sum of squares, Positivstellensatz, theory of moments, Pólya's theorem, and matrix dilation. Moreover, it aims to provide a collection of the essential problems in control systems where these LMI techniques are used, such as stability and performance investigations in nonlinear systems, uncertain systems, time-delay systems, and genetic regulatory networks. It is expected that this survey may be a concise useful reference for all readers.
Sponsorship	IEEE Control Systems Society
Starting Page	2500
Ending Page	2510
Page Count	11
File Size	337353
File Format	PDF
ISSN	00189286
Volume Number	55
Issue Number	11
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-11-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Polynomials Control systems Linear matrix inequalities Stability Control system synthesis Lyapunov method Matrix decomposition Nonlinear control systems Nonlinear systems Uncertain systems positivity Control system linear matrix inequality (LMI) optimization polynomial
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Electrical and Electronic Engineering Computer Science Applications

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