Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2012, Article ID 315049, 21 pages doi:10.1155/2012/315049 Research Article Less Conservative Control Design for Linear Systems with Polytopic Uncertainties via State-Derivative Feedback Emerson R. P. da Silva, Edvaldo Assunc ¸˜ ao, Marcelo C. M. Teixeira, and Luiz Francisco S. Buzachero Research Laboratory in Control, Department of Electrical Engineering, Univ Estadual Paulista (UNESP), Campus de Ilha Solteira, Avenue Jos´ e Carlos Rossi, no 1370, 15385-000 Ilha Solteira, SP, Brazil Correspondence should be addressed to Emerson R. P. da Silva, e.ravazzi@bol.com.br Received 4 August 2011; Accepted 20 October 2011 Academic Editor: F. Lobo Pereira Copyright q 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. 1. Introduction In studies of classical control theory, it is well known that the use of state-derivative feedback ut -K d ˙ xt can be very useful, and in some cases, essential and advantageous for achieving desired performance in dynamic systems 1. The interest to study the state- derivative feedback comes from the fact that in systems using accelerometers, it is easier to get the state-derivatives signals than the states signals. Using the acceleration signal, the velocity can be obtained with good accuracy. However, it is more difficult to obtain the displacement 2. Thus, the signals used in feedback are: velocity and acceleration. Respectively, these are the derivatives of position and velocity that can represent the system states. Due to its simple structure and low operating cost, accelerometers have been used in industry for solving various engineering problems. For example, they can give some applications: in vibration control of suspension bridges cables 3, in vibration control of components for aircraft