Abstract— A robust tracking fuzzy control technique for nonlinear time-delay systems based on fuzzy T-S model is proposed. The fuzzy T-S system model with parametric uncertainties is employed to represent a nonlinear time-delay plant. The control design synthesis is aimed to reduce to negligible small the tracking error for all bounded reference inputs and to guarantee ∞ H performance. The advantage of proposed tracking control design is only a simple fuzzy controller designs are employed. By means of the proposed method, the fuzzy tracking control design problem is parameterized in terms of a linear matrix inequality problem, which can be efficiently solved using any convex optimization techniques. The example of trucking control for the benchmark truck-trailer system is given to demonstrate the efficiency as well as the validity of the proposed technique. I. INTRODUCTION HE tasks of stabilization and of tracking control of dynamical processes are two basic problems of control systems engineering. In general, the tracking problems are more difficult than stabilization problems especially for the cases of essentially nonlinear systems. For nonlinear systems design, various control schemes, based on both math- analytical and fuzzy-computing models, have been introduced including exact feedback linearization, siding model control, and adaptive control to name a few. The technique of exact feedback linearization may well be rather effective. However, it known to need perfect knowledge of the nonlinear plant system because it makes use of that knowledge to cancel the nonlinearities of the system. Furthermore, as pointed out in [1], the controller derived by feedback linearization may not be bounded; in other words, the fuzzy controller is not guaranteed to be stable for non-minimum phase systems. Besides, the perfect plant knowledge in the technique of exact feedback linearization appeared rather impractical for nonlinear system design [2, 3]. Still based on the idea of feedback Manuscript received January 31, 2006. This work was supported in part by grants from the respective funds of Northeastern University of Shenyang, P. R. of China, Dogus University of Istanbul, R. of Turkey, and SS Cyril and Methodius University of Skopje, r. of Macedonia. Georgi M. Dimirovski (the correspondence author) is with Dogus University, Faculty of Engineering, Department of Computer Engineering Acibadem – Kadikoy, Istanbul, 34722, R. of Turkey, and with SS Cyril and Methodius University, Skopje, MK-1000, R. of Macedonia (e-mail: gdimirovski @dogus.edu.tr). Yuan-Wei Jing and Xin-Jiang Wei are with Northeastern University, School of Information Science and Engineering, Institute of Control Science, Shenyang, Liaoning Province,, 110004, P. R. of China (e-mails: ywjing@mail.neu.edu.cn ; weixinjian@eyou.com. linearization technique, ∞ H adaptive fuzzy control schemes have been also introduced to deal with nonlinear systems [4, 5]. However, typically complicated parameter update law and control algorithms often renders this control scheme also impractical. This is especially the case in conjunction with considering the projection algorithm for the parameter update law to avoid the singularity of feedback linearization control. In the case of sliding mode control schemes, an important advantage is found in its robustness to uncertainties [6]. However, the chattering phenomenon is inevitable in the sliding mode control schemes, which in turn often may cause high heat loss in actuator electrical power circuits and low control accuracy too. Recently, Takagi–Sugeno (T–S) type fuzzy controllers have been successfully applied to the stabilization control problems in various nonlinear systems [7-9]. In most of these applications, the fuzzy systems were thought of as a universal approximation for the nonlinear system of concern. The T–S fuzzy model has been proved to be a very good representation for a certain class of nonlinear dynamic systems [7]. In their studies, a nonlinear plant was represented by a set of linear models interpolated by membership functions T–S fuzzy model and then a model- based fuzzy controller was developed to stabilize the T–S fuzzy model. On the other hand, tracking control designs are also important issues for practical applications [10, 11], such as in robotic tracking control, missile tracking control and attitude tracking control of aircraft. However, there are very few studies concerning with tracking control design based on the T–S fuzzy model, especially for continuous-time systems. Tseng et al. [10] proposed fuzzy tracking control design for nonlinear dynamic systems visa T–S fuzzy model. However their work did only concern on the tracking control of nominal T–S fuzzy model without time-delay and uncertainty. So the robustness of the whole control tracking control system cannot be guaranteed. Dynamical systems with time delay are common in chemical processes and long transmission lines in pneumatic, hydraulic, or rolling mill systems. Nonlinear systems with time delay constitute basic mathematical models of real phenomena in biology, mechanics, economics, etc. Generally speaking, the dynamic behaviors of systems with delays are more complicated than that of systems without any delays. Fuzzy delayed systems of T–S model provide a method of using local linear delayed systems combined with fuzzy linguistic descriptions to achieve nonlinearity. Motivated by the aforementioned concerns, this paper develops a novel robust tracking control design for nonlinear time-delay systems, which makes use of Linear Synthesis of Fuzzy Tracking Control for Nonlinear Time-Delay Systems Georgi M. Dimirovski, Senior Member, IEEE, Yuan-Wei Jing, and Xin-Jiang Wei T 0-7803-9489-5/06/$20.00/©2006 IEEE 2006 IEEE International Conference on Fuzzy Systems Sheraton Vancouver Wall Centre Hotel, Vancouver, BC, Canada July 16-21, 2006 7545