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Technical Brief

Calculating Positive Invariant Sets: A Quantifier Elimination Approach

[+] Author and Article Information
Klaus Röbenack

Professor, Institute of Control Theory, Faculty of Electrical and Computer Engineering, Technische Universität Dresden, 01062 Dresden, Germany
klaus.roebenack@tu-dresden.de

Rick Voßwinkel

PhD Student, Institute of Control Theory, Faculty of Electrical and Computer Engineering, Technische Universität Dresden, 01062 Dresden, Germany
rick.vosswinkel@htwk-leipzig.de

Hendrik Richter

Professor, Faculty of Electrical Engineering and Information Technology, HTWK Leipzig University of Applied Sciences, 04107 Leipzig, Germany
hendrik.richter@htwk-leipzig.de

1Corresponding author.

ASME doi:10.1115/1.4043380 History: Received November 12, 2018; Revised March 27, 2019

Abstract

A Lyapunov-based approach for calculating positive invariant sets in an automatic manner is presented. This is done using real algebraic geometry techniques which are summed up under the term quantifier elimination. Using available tools the approach presented yields an algorithmizable procedure whose conservatism only depends on the initial choice for the Lyapunov candidate function. The performance of the approach is illustrated on a variant of the R\"ossler system and on the Lorenz-Haken system.

Copyright (c) 2019 by ASME
Topics: Geometry , Algebra
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