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Journal of Control Science and Engineering
Volume 2015 (2015), Article ID 720203, 10 pages
Research Article

Less Conservative Optimal Robust Control of a 3-DOF Helicopter

1Universidade Tecnológica Federal do Paraná (UTFPR), 86812-460 Apucarana, PR, Brazil
2Research Laboratory in Control, Department of Electrical Engineering, Universidade Estadual Paulista (UNESP), Campus of Ilha Solteira, 15385-000 Ilha Solteira, SP, Brazil
3Universidade Tecnológica Federal do Paraná (UTFPR), 86300-000 Cornélio Procópio, PR, Brazil

Received 6 October 2014; Accepted 14 January 2015

Academic Editor: Yongji Wang

Copyright © 2015 L. F. S. Buzachero 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 work proposes an improved technique for design and optimization of robust controllers norm for uncertain linear systems, with state feedback, including the possibility of time-varying the uncertainty. The synthesis techniques used are based on LMIs (linear matrix inequalities) formulated on the basis of Lyapunov’s stability theory, using Finsler’s lemma. The design has used the addition of the decay rate restriction, including a parameter γ in the LMIs, responsible for decreasing the settling time of the feedback system. Qualitative and quantitative comparisons were made between methods of synthesis and optimization of the robust controllers norm, seeking alternatives with lower cost and better performance that meet the design restrictions. A practical application illustrates the efficiency of the proposed method with a failure purposely inserted in the system.