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Journal of Control Science and Engineering
Volume 2011 (2011), Article ID 273469, 7 pages
Research Article

The Kronecker Summation Method for Robust Stabilization Applied to a Chemical Reactor

1Department of Automation and Control Engineering, Faculty of Applied Informatics, Tomas Bata University in Zlín, nám. T. G. Masaryka 5555, 760 01 Zlín, Czech Republic
2Department of Information Engineering and Process Control, Faculty of Chemical and Food Technology, Slovak University of Technology in Bratislava, Radlinského 9, 812 37 Bratislava, Slovakia

Received 29 September 2010; Revised 12 January 2011; Accepted 30 March 2011

Academic Editor: Ricardo S. Sánchez Peña

Copyright © 2011 Radek Matušů et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper focuses on robust stabilization where the suitable parameters of a simple continuous-time PI controller are determined through a combination of the Kronecker summation method, sixteen plant theorem, and an algebraic approach to control design in the ring of proper and stable rational functions. The initial theoretical background is followed by an illustrative experiment which includes computation of the controller and verification of control results for a continuous stirred tank reactor with exothermic reaction modelled as a fourth-order interval system.