Control design for a 2 ⊗ 2 hyperbolic system with application to preferential crystallization

This paper deals with a mathematical model of the preferential crystallization of enantiomers. The dynamics is governed by two first‐order partial differential equations with controls appearing in the coefficients and in the boundary conditions. We study the problem of stabilizing the equilibrium of...

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Bibliographic Details
Published inProceedings in applied mathematics and mechanics Vol. 18; no. 1
Main Authors Zuyev, Alexander, Benner, Peter
Format Journal Article
LanguageEnglish
Published Berlin WILEY‐VCH Verlag 01.12.2018
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Summary:This paper deals with a mathematical model of the preferential crystallization of enantiomers. The dynamics is governed by two first‐order partial differential equations with controls appearing in the coefficients and in the boundary conditions. We study the problem of stabilizing the equilibrium of this system by a one‐dimensional input. For this purpose we construct a Lyapunov functional in the integral form whose density is defined through solutions of auxiliary ordinary differential equations. It is shown that the time derivative of this functional along the trajectories of the closed‐loop system is negative semidefinite. We also discuss some extensions of these results for the construction of a strict Lyapunov functional.
ISSN:1617-7061
1617-7061
DOI:10.1002/pamm.201800455