Construction of a Lyapunov functional for a class of controlled population balance models |
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| Authors: | Alexander Zuyev Achim Kienle Peter Benner |
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| Affiliation: | 1. Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany;2. Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany Otto von Guericke University, Magdeburg, Germany |
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| 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 L2-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) |
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