ROBUST OUTPUT FEEDBACK CONTROLLER DESIGN VIA GENETIC ALGORITHM Ivan Sekaj and Vojtech Vesel´ y 1 Department of Automatic Control Systems, Slovak University of Technology in Bratislava, Ilkoviˇ cova 3, 81219 Bratislava, Slovak Republic. E-mail: sekaj@kasr.elf.stuba.sk; vesely@kasr.elf.stuba.sk Abstract: This paper proposes guaranteed cost design of robust output feedback controller for continuous linear parametric uncertain systems. Proposed algorithms are computationally simple and tightly connected with the Lyapunov stability theory and the LQR optimal state feedback design. The proposed approach allows for prescribing the structure of the output feedback gain matrix (including the decentralized one) by the designer. New design method proposed in this paper, exploit genetic algorithm to design robust controller with guaranteed cost for polytopic linear continuous time systems. Numerical example is given to illustrate the performance of the proposed robust controller. Keywords: Robust controller, Linear systems, Genetic algorithm 1. INTRODUCTION In the excellent survey on static output feedback controller design in (Syrmos et al,1997 ) is stated that the static output feedback problem is one of the most important open questions in con- trol engineering. Simply stated, the problem is as follows: given a dynamic system, find a static output feedback so that the closed loop system has some desirable characteristics. During the last two decades numerous papers dealing with the design of robust output feedback control schemes have been published ( Benton and Smith, 1999; El Ghaoui and Balakrishnam, 1994; Imai, 1997; Iwasaki, Skelton and Geromel, 1994; Kose and Jabbari, 1999; Koz´ak, 1995; Li Yu and Jian Chu, 1999; Xu and Darouch, 1998; Yong Yan Gao and You Xian Sun, 1998; Vesel´ y and Sekaj, 2000; Hei Ke Tam and Lam,1999). Various approaches have been applied to study the two aspects of this sta- bilization problem, namely the conditions under 1 This work was supported by the Slovak Grant Agency under Grants N 1/7608/20 and 1/7128/20. which a linear system described in the state space can be stabilized via output feedback and the respective procedure for obtaining a stabilizing control law (Kuˇ cera and De Souza, 1995; Syrmos et al,1997). In the above papers, the authors ba- sically conclude that despite the availability of many approaches and numerical algorithms the static output feedback problem is still open. This is justified by the fact that up to now there are no testable necessary and sufficient conditions avail- able to test stability of a static output feedback system. Recently it has been shown that an extremely wide array of robust controller design problems can be reduced to the problem of finding a feasible point under a Biaffine Matrix Inequality (BMI) constraint. The BMI has been introduced in (Goh et al, 1995) as a geometric reformulation of many robust control problems. However it is known that BMI problems are NP-hard (Toker and Ozbay , 1995). The main result of (Toker and Ozbay , 1995) shows that it is rather unlikely to find an algorithm for solving general BMI problems and it has also been shown that simultaneous stabiliza- Copyright © 2002 IFAC 15th Triennial World Congress, Barcelona, Spain