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Analysis of Non-polynomial Systems Using the Sum of Squares Decomposition

Papachristodoulou, Antonis and Prajna, Stephen (2005) Analysis of Non-polynomial Systems Using the Sum of Squares Decomposition. In: Positive Polynomials in Control. Lecture Notes in Control and Information Science. No.312. Springer , Berlin, pp. 23-43. ISBN 978-3-540-23948-2.

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Recent advances in semidefinite programming along with use of the sum of squares decomposition to check nonnegativity have paved the way for efficient and algorithmic analysis of systems with polynomial vector fields. In this paper we present a systematic methodology for analyzing the more general class of non-polynomial vector fields, by recasting them into rational vector fields. The sum of squares decomposition techniques can then be applied in conjunction with an extension of the Lyapunov stability theorem to investigate the stability and other properties of the recasted systems, from which properties of the original, non-polynomial systems can be inferred. This will be illustrated by some examples from the mechanical and chemical engineering domains.

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Additional Information:© 2005 Springer-Verlag Berlin Heidelberg. First Online: 04 August 2005. The authors contributed equally to this work. The authors would like to acknowledge the input of Professors Michael Savageau and John C. Doyle.
Subject Keywords:Lyapunov Function; Continuously Stir Tank Reactor; Polynomial Vector; Lyapunov Function Versus; Saturation Nonlinearity
Series Name:Lecture Notes in Control and Information Science
Issue or Number:312
Record Number:CaltechAUTHORS:20200107-155428126
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100548
Deposited By: Tony Diaz
Deposited On:08 Jan 2020 18:26
Last Modified:16 Nov 2021 17:54

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