Advances in Difference Equations
Volume 2010 (2010), Article ID 108218, 15 pages
doi:10.1155/2010/108218
Control of oscillating systems with a single delay
J. Diblík
, D.Ya. Khusainov2
, J. Lukáčová3
and M. Růžičková3
2Department of Complex System Modeling, Faculty of Cybernetics, Taras Shevchenko National University of Kyiv, 01033 Kyiv, Ukraine
3Department of Mathematics, The Faculty of Science, The University of {Z}ilina, 01026 {Z}ilina, Slovakia
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.