Construction of a Lyapunov functional for a class of controlled population balance models. Issue 1 (15th March 2018) - Zuyev, Alexander; Kienle, Achim; Benner, Peter
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)