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Mathematical Problems in Engineering
Volume 2013, Article ID 595029, 10 pages
Research Article

On Switched Control Design of Linear Time-Invariant Systems with Polytopic Uncertainties

1Department of Academic Areas of Jataí, Federal Institute of Education, Science and Technology of Goiás (IFG), Campus Jataí, 75804-020 Jataí, GO, Brazil
2Department of Electrical Engineering, UNESP, Univ Estadual Paulista, Campus de Ilha Solteira, 15385-000 Ilha Solteira, SP, Brazil
3Department of Computer, Telecommunication, Control, and Automation Engineering, Faculdade of Science and Technology of Montes Claros (FACIT), Campus II, 39400-141 Montes Claros, MG, Brazil

Received 17 January 2013; Accepted 12 April 2013

Academic Editor: Oleg V. Gendelman

Copyright © 2013 Wallysonn A. de Souza 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.


This paper proposes a new switched control design method for some classes of linear time-invariant systems with polytopic uncertainties. This method uses a quadratic Lyapunov function to design the feedback controller gains based on linear matrix inequalities (LMIs). The controller gain is chosen by a switching law that returns the smallest value of the time derivative of the Lyapunov function. The proposed methodology offers less conservative alternative than the well-known controller for uncertain systems with only one state feedback gain. The control design of a magnetic levitator illustrates the procedure.