Advances in Difference Equations
Volume 2010 (2010), Article ID 108218, 15 pages
doi:10.1155/2010/108218
Research Article
Control of Oscillating Systems with a Single Delay
1Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, 66237 Brno, Czech Republic
2Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 61600 Brno, Czech Republic
3Department of Complex System Modeling, Faculty of Cybernetics, Taras Shevchenko National University of Kyiv, 01033 Kyiv, Ukraine
4Department of Mathematics, The Faculty of Science, The University of Žilina, 01026 Žilina, Slovakia
Received 1 December 2009; Accepted 29 January 2010
Academic Editor: Ağacik Zafer
Copyright © 2010 J. Diblík 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.
Abstract
Systems are considered related to the control of processes described by oscillating second-order systems of differential equations with a single delay. An explicit representation of solutions with the aid of special matrix functions called a delayed matrix sine and a delayed matrix cosine is used to develop the conditions of relative controllability and to construct a specific control function solving the relative controllability problem of transferring an initial function to a prescribed point in the phase space.