Robust sliding mode controllers design techniques for stabilization of multivariable time-delay systems with parameter perturbations and external disturbances

Abstract

Abstract In this paper, robust delay-independent stabilization of multivariable single state-delayed systems with mismatching parameter uncertainties and matching/mismatching external disturbances are considered. To achieve this goal, two types of robust sliding mode controllers design techniques are advanced. The first is an integral sliding mode controller design modification to Shyu and Yan type controller design. The mismatching sliding conditions are parametrically obtained by using the Lyapunov-Razumikhin-Hale method and formulated in terms of some matrix norm inequalities. In the second contribution, a new combined sliding mode controller design technique for the stabilization of multivariable single state-delayed systems with mismatching parameter perturbations is advanced by using the Lyapunov-Krasovskii V-functional method. The sliding, global stability and delay-dependent β-stability conditions are parametrically obtained and formulated in terms of matrix inequalities. A sliding mode controller design example for AV-8A Harrier VTOL aircraft with lateral unstable dynamic model parameters is considered to illustrate the controller design method. Design procedures and simulation results show that our advanced method is useful, and unstable lateral dynamics is successfully stabilized by using the combined controller. Keywords: Sliding mode controllerIntegral switching surfaceStability conditionsRobust stabilizationTime-delay systemsMismatching perturbations Acknowledgements The author would like to thank the Senior Editor of Journal, dear Prof. Peter Fleming, the Associate Editor and Referees 1, 2 and 3 for the constructive criticism, valuable comments and suggestions, tolerance and discussion opportunity providing the improvement of the article. Elbrous M. Jafarov was born in province Gokche, village Karkibash in the west of Azerbaijan in 1946. He received his first class Honors Electro-Mechanical Eng. Diploma (M.Sc. Degree) in Automation of Manufacturing Process from Azerbaijan Industrial University, Baku, Azerbaijan in 1969. The USSR State Certification of Candidate Eng. Sc. (Ph.D.) and D.Sc. (Eng) degrees from Research Institute NIPINefteKhimAutomat (Sumgait)-TsNIIKAutomation (Moscow)- IMM and Institute of Cybernetics of Azerbaijan Science Academy and Institute of Control Sciences (Moscow)-MIEM-LETI in Control Engineering were received in 1973 and 1982, respectively. He started as a research engineer in NIPINefteKhimAutomat and then he became Head of Variable Structure Control of the Oil-Chemical Process Laboratory from 1969 to 1984. During 1985-1996 he was Chairman of the Control Systems and Robotics Engineering Department at the Azerbaijan Technical University, Baku. Dr. Jafarov received the USSR State Certification of Professor in Control System Engineering in 1987. He was visiting Professor at Beijing Aeronautical and Astronautical University (BUAA), China, 1993. He has been contractual Professor in the Aeronautical and Astronautical Department of Istanbul Technical University, Turkey, since 1996. He is senior student of University of Allah, Virginia USA. Professor Jafarov is the author of about 200 scientific journal articles, international conference papers, and 27 inventions in Control Engineering. He is a member of IASTED (Canada), WSEAS (Greece), Int. Tech. Cybernetics Academy (Saint Petersburg), Literature Club (London) etc. His current research interests include variable structure control, time delay systems, flight control, robust control etc. He is also interested in relativity theory, poetry and sufism. Notes Email: cafer@itu.edu.tr Additional informationNotes on contributorsElbrous M. Jafarov Footnote* Email: cafer@itu.edu.tr