Construction of a Lyapunov functional for a class of controlled population balance models. Issue 1 (15th March 2018)

• Record Type: Journal Article
• Authors: Zuyev, Alexander; Kienle, Achim; Benner, Peter
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 17:Issue 1(2017)
• Page Start: 827
• Page End: 828
• Publication Date: 2018-03-15
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201710381
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: 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)