Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 315049, 21 pages
Research Article

Less Conservative Control Design for Linear Systems with Polytopic Uncertainties via State-Derivative Feedback

Research Laboratory in Control, Department of Electrical Engineering, Univ Estadual Paulista (UNESP), Campus de Ilha Solteira, Avenue José Carlos Rossi, no 1370, 15385-000 Ilha Solteira, SP, Brazil

Received 4 August 2011; Accepted 20 October 2011

Academic Editor: F. Lobo Pereira

Copyright © 2012 Emerson R. P. da Silva 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 motivation for the use of state-derivative feedback instead of conventional state feedback is due to its easy implementation in some mechanical applications, for example, in vibration control of mechanical systems, where accelerometers have been used to measure the system state. Using linear matrix inequalities (LMIs) and a parameter-dependent Lyapunov functions (PDLF) allowed by Finsler’s lemma, a less conservative approach to the controller design via state-derivative feedback, is proposed in this work, with and without decay rate restriction, for continuous-time linear systems subject to polytopic uncertainties. Finally, numerical examples illustrate the efficiency of the proposed method.