Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2013, Article ID 595029, 10 pages http://dx.doi.org/10.1155/2013/595029 Research Article On Switched Control Design of Linear Time-Invariant Systems with Polytopic Uncertainties Wallysonn A. de Souza, 1 Marcelo C. M. Teixeira, 2 Máira P. A. Santim, 3 Rodrigo Cardim, 2 and Edvaldo Assunção 2 1 Department of Academic Areas of Jata´ ı, Federal Institute of Education, Science and Technology of Goi´ as (IFG), Campus Jata´ ı, 75804-020 Jata´ ı, GO, Brazil 2 Department of Electrical Engineering, UNESP, Univ Estadual Paulista, Campus de Ilha Solteira, 15385-000 Ilha Solteira, SP, Brazil 3 Department of Computer, Telecommunication, Control, and Automation Engineering, Faculdade of Science and Technology of Montes Claros (FACIT), Campus II, 39400-141 Montes Claros, MG, Brazil Correspondence should be addressed to Wallysonn A. de Souza; wallysonn@yahoo.com.br Received 17 January 2013; Accepted 12 April 2013 Academic Editor: Oleg V. Gendelman Copyright © 2013 Wallysonn A. de Souza et al. Tis 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. Tis paper proposes a new switched control design method for some classes of linear time-invariant systems with polytopic uncertainties. Tis method uses a quadratic Lyapunov function to design the feedback controller gains based on linear matrix inequalities (LMIs). Te controller gain is chosen by a switching law that returns the smallest value of the time derivative of the Lyapunov function. Te proposed methodology ofers less conservative alternative than the well-known controller for uncertain systems with only one state feedback gain. Te control design of a magnetic levitator illustrates the procedure. 1. Introduction In recent years, there has been much interest in studying switched systems, due to the considerable advance in this research feld, initiating mainly with [1–4]. For linear time- invariant systems, the transient response can be improved through switching controllers [5], as can be seen, for instance, in [6–9]. In general, most papers in the area of switched linear systems utilize multiple Lyapunov functions [10–14]. A design method that is applicable to a large class of switched con- trollers for linear systems with input signals, formulated with bilinear matrix inequalities (BMIs), is proposed in [10]. Te switching law defnes regions where diferent subsystems are activated, resulting in a switched linear system that is exponentially stable. Study results on the stability analysis and stabilization of switched systems can be seen in [11], which presents necessary and sufcient conditions for asymptotic stability. Moreover, the problem of switching stabilizability is studied, investigating under what conditions it is possible to stabilize a switched system by designing switching control laws. Necessary and sufcient conditions for switched linear systems with polytopic uncertainties to be quadratically stabilizable via state feedback can be found in [13]. Te design of the robust state feedback control for continuous-time systems subject to norm bounded uncer- tainty can be seen in [12], where the switching rule, as well as the state feedback gains, is determined from the minimization of a guaranteed cost function derived from a multiobjective criterion. Te paper [14] presents a general- ization of the results proposed in [12] and ofers a procedure that fnds, simultaneously, a set of state feedback gains and a switching rule to orchestrate them, rendering the equilibrium point of closed-loop system globally asymptotically stable for all time-varying uncertain parameters under consideration and assuring a guaranteed H 2 cost. Although outnumbered, there are papers about switched linear systems using a common Lyapunov function as in [15, 16]. In [15], the stability of switched linear systems with polytopic uncertainties was studied. Some criteria for globally