Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2013, Article ID 537414, 6 pages http://dx.doi.org/10.1155/2013/537414 Research Article Observer-Based Sliding Mode Control for Stabilization of a Dynamic System with Delayed Output Feedback Bo Wang, 1,2 Peng Shi, 3,4 Hamid Reza Karimi, 5 and Cheng Chew Lim 3 1 School of Applied Mathematics, University Electronic Science and Technology of China, Chengdu 610054, China 2 School of Electrical and Information Engineering, Xihua University, Chengdu 610096, China 3 School of Electrical and Electronic Engineering, he University of Adelaide, Adelaide, SA 5005, Australia 4 College of Engineering and Science, Victoria University, Melbourne, VIC 8001, Australia 5 Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway Correspondence should be addressed to Hamid Reza Karimi; hamid.r.karimi@uia.no Received 10 July 2013; Accepted 29 August 2013 Academic Editor: Rongni Yang Copyright © 2013 Bo Wang et al. his 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. his paper considers the sliding mode control problem for a kind of dynamic delay system. First by utilizing Lyapunov stability theory and a linear matrix inequality technique, an observer based on delayed output feedback is constructed. hen, an integral sliding surface is presented to realize the sliding mode control for the system with the more available stability condition. Finally, some numerical simulations are implemented to demonstrate the validity of the proposed control method. 1. Introduction For system control, state feedback control is a powerful tool when the full information of the system states is assumed to be accessible. However, in real engineering, not all of them can be available. Hence, the research on observer-based con- trol system is a meaningful topic. Up to now, many relevant investigations [1–10] have been carried out. For instance, in [1], by imposing some restrictions on an open-loop system, two classes of the observer-based output feedback controllers, one inite dimensional and the other one ininite dimen- sional, are constructed; in [2], a static gain observer for linear continuous plants with intrinsic pulse-modulated feedback is designed to asymptotically drive the state estimation error to zero; in [3], by using the orthogonality-preserving numerical algorithm, a nonlinear discrete-time partial state observer is designed to realize the attitude determination for a kind of spacecrat system; in [4], with the two-step observation algo- rithms, an observer is constructed to force an underactuated aircrat to asymptotically track a given reference trajectory; in [5], through employing an adaptive backstepping approach, a modiied high-gain observer is introduced to realize the global asymptotic tracking for a class of nonlinear systems. In real engineering, time delays exist objectively, which makes the observer-based system control issue more com- plicated. Many existing control methods that have been well developed based on the conventional feedback observer, such as ones in [1–5], are not directly applicable. In addition, the LMI technique is known as a powerful tool for system control. However, it is not easy to use any more when time delays appear in the feedback output of system. Hence, the cor- responding research is meaningful. Sliding mode control (SMC) has been proven to be an efective robust control strat- egy and has been successfully applied to a wide range of engi- neering systems such as spacecrats, robot manipulators, air- crat, underwater vehicles, electrical motors, power systems, and automotive engines [11–25]. In [11], a novel integral slid- ing surface is introduced to achieve the control for a kind of system based on the LMI technique, with the more available stability condition compared to the conventional linear slid- ing surface. However, the system with delay is not included in its research yet. Hence, all of the above motivate our work. In this paper, the problem on the SMC for a kind of delay dynamic system will be discussed. By utilizing Lyapunov stability theory and a linear matrix inequality technique, a new observer-based on delayed output feedback will be