Asian Journal of Control, Vol. 7, No. 2, pp. 99-111, June 2005 99 Manuscript received April 22, 2003; revised February 4, 2004; accepted May 22, 2004. Péter Baranyi is with the Computer and Automation Re- search Institute of the Hungarian Academy of Sciences, H-1111 Budapest, Kendeu. 13-17, Hungary (e-mail: baranyi@ tmit.ttt.bme.hu). Péter Korondi and Hideki Hashimoto are with the Integrated Intelligent Systems Japanese-Hungarian Laboratory, Budapest University of Technology and Economics, H-1111 Budapest, Műegyetem rakpart 3, Hungary (e-mails: baranyi@tmit.ttt. bme,hu, korondi@elektro.get.bme.hu). This work was supported by the Hungarian National Found OTKA 049838. GLOBAL ASYMPTOTIC STABILIZATION OF THE PROTOTYPICAL AEROELASTIC WING SECTION VIA TP MODEL TRANSFORMATION Péter Baranyi, Péter Korondi, and Hideki Hashimoto ABSTRACT A comprehensive analysis of aeroelastic systems has shown that these systems exhibit a broad class of pathological response regimes when certain types of non-linearities are included. In this paper, we propose a design method of a state-dependent non-linear controller for aeroelastic systems that includes polynomial structural non-linearities. The proposed method is based on recent numerical techniques such as the Tensor Product (TP) model transformation and the Linear Matrix Inequality (LMI) control de- sign methods within the Parallel Distributed Compensation (PDC) frame- works. In order to link the TP model transformation and the LMI’s in the proposed design method, we extend the TP model transformation with a further transformation. As an example, a controller is derived that ensures the global asymptotic stability of the prototypical aeroelastic wing section via one control surface, in contrast with previous approaches which have achieved local stability or applied additional control actuator on the purpose of achieving global stability. Numerical simulations are used to provide empirical validation of the control results. The effectiveness of the control- ler design is compared with a former approach. KeyWords: Aeroelasticity, tensor product model transformation, linear matrix inequality, parallel distributed compensation. I. INTRODUCTION In the past few years various studies of aeroelastic systems have emerged. [1] presents a detailed background and refers to a number of papers dealing with the modelling and control of aeroelastic systems. The following provides a brief summary of this background. Regarding the properties of aeroelastic systems one can find the study of free-play non-linearity by Tang and Dowell in [2,3], by Price et al. in [4] and [5], by Lee et al. in [6], and a complete study of a class of non-linearities is in [7], [5]. O’Neil et al. [8] examined the continuous struc- tural non-linearity of aeroelastic systems. These papers conclude that an aerolesatic system may exhibit a variety of control phenomena such as limit cycle oscillation, flutter and even chaotic vibrations. Control strategies have also been derived for aeroelas- tic systems. [9] shows that controllers, capable of stabiliz- ing structural non-linearity over flow regimes, can be de- rived via classical multivariable control methods. However, while several authors have investigated the effectiveness of linear control strategies for aeroelastic systems, experi- mental evidence has shown that linear control methods may not be reliable when non-linear effects predominate. For example in the case of large amplitude limit cycle oscilla-