Research Article A Solution for the Generalized Synchronization of a Class of Chaotic Systems Based on Output Feedback Carlos Aguilar-Ibanez, 1 R. Martínez-Guerra, 2 C. Pérez-Pinacho, 2 E. García-Canseco, 3 and Miguel S. Suarez-Castanon 4 1 Instituto Polit´ ecnio Nacional-CIC, Avenida Juan de Dios B´ atiz, s/n, 07738 M´ exico, DF, Mexico 2 Department of Automatic Control, CINVESTAV-IPN, Avenida Instituto Polit´ ecnico Nacional 2508, 07360 M´ exico, DF, Mexico 3 Faculty of Sciences, Autonomous University of Baja California, Km. 103 Carretera Tijuana-Ensenada, 22860 Ensenada, BCN, Mexico 4 Instituto Polit´ ecnio Nacional-ESCOM, Avenida Juan de Dios B´ atiz Esquina Miguel Oth´ on de Mendiz´ abal, 07738 M´ exico, DF, Mexico Correspondence should be addressed to Carlos Aguilar-Ibanez; carlosaguilari@cic.ipn.mx Received 9 June 2015; Revised 4 September 2015; Accepted 6 September 2015 Academic Editor: Rafael Morales Copyright © 2015 Carlos Aguilar-Ibanez et al. is 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. A solution to the output-feedback generalized synchronization problem for two chaotic systems, namely, the master and the slave, is presented. e solution assumes that the slave is controlled by a single input, and the states of each system are partially known. To this end, both systems are expressed in their corresponding observable generalized canonical form, through their differential primitive element. e nonavailable state variables of both systems are recovered using a suitable Luenberger observer. e convergence analysis was carried out using the linear control approach in conjunction with the Lyapunov method. Convincing numerical simulations are presented to assess the effectiveness of the obtained solution. 1. Introduction e synchronization of strictly different chaotic systems is a current challenge in Control eory. In general, accom- plishing and understanding this kind of synchronization, referred to as generalized synchronization (GS), are a difficult problem and are very important because its solution can be useful to actual applications. For instance, chaotic signals have been used in secure information transmission. In this regard, interesting secure communication methods based on GS can be found in the literature. In [1], a channel- independent chaotic secure communication scheme based on GS is proposed. A similar scheme, also based on GS, with a remarkable stability to noise and numerically validated using the R¨ ossler system is developed in [2]. Two novel generalized chaos synchronization based secure communication schemes are introduced in [3, 4]. e first scheme is complemented with a transposition function and is tested using the Chen chaotic circuit; the second scheme is oriented to encrypt images and uses a theorem introduced by the authors, which is a generalization of GS to an array of differential equations. From a theoretical point of view, synchronization of strictly different chaotic systems helps to explain how some oscillatory systems, like the intrinsic neuron model, act cooperatively to develop tasks or solve problems [5]. is behavior also occurs in nature and can be responsible for the transition to low-dimensional behavior in systems with many degrees of freedom. A full review of GS is beyond the scope of this study; however, we mention two seminal works. In [6] the authors developed a method for decomposing chaotic systems such that linear GS can be achieved. Finally, we mention work [5], where the authors proposed a method used to detect and study generalized synchronization in drive- response systems. e method uses an identical response system to monitor the synchronized motions. We suggest to the interested reader the following list of remarkable works [7–16]. Loosely speaking the GS phenomenon occurs when the trajectories of one system, through a functional mapping, are equal to trajectories of another. In other words, let us suppose Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2015, Article ID 848203, 11 pages http://dx.doi.org/10.1155/2015/848203