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Construction of a Lyapunov functional for a class of controlled population balance models
Author(s) -
Zuyev Alexander,
Kienle Achim,
Benner Peter
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710381
Subject(s) - lyapunov function , mathematics , class (philosophy) , population , norm (philosophy) , stability theory , balance (ability) , nonlinear system , computer science , physics , medicine , demography , quantum mechanics , artificial intelligence , sociology , physical medicine and rehabilitation , political science , law
In this paper, we consider a class of controlled population balance equations describing granulation processes in chemical engineering. Such a control system admits an equilibrium which is not asymptotically stable in general. In order to stabilize this equilibrium, we consider the perturbed system and introduce a Lyapunov functional candidate as a weighted L 2 ‐norm. It is shown that the weight function for this construction may be defined in terms of solutions to a certain differential inequality. We present a solution of this differential inequality in a particular case and discuss possible extensions of this approach for multidimensional hyperbolic systems. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)