Stabilizing adaptive controller for uncertain dynamical systems: An LMI approach

Adaptive stabilization of a class of linear systems with matched and unmatched uncertainties is considered in this paper. The proposed controller indeed stabilizes the uncertain system for any positive values of its non-adaptive gain that may be tuned to enhance dynamic response of system. The performance of uncertain system along with the Algebraic Riccati Equation that arises from the adaptive stabilizing controller is now formulated as a multi-objective Linear Matrix Inequality optimization problem. The decay rate and a factor governing the ultimate bound of the system states are considered to characterize the closed loop system performance. Finally, the effectiveness of the proposed controller is illustrated via stabilizing a mass-spring system. Recommended by Editorial Board member Gang Tao under the direction of Editor Young Il Lee. The authors would like to thank the reviewers for their valuable comments and suggestions that have improved the quality of this paper. Sandip Ghosh received the B.E. in Electrical Engineering from Bengal Engineering College (D.U.), Howrah, and Master in Control System Engineering from Jadavpur University, Kolkata, India, in 1999 and 2003 respectively. Presently he is pursuing the Ph.D. degree at Indian Institute of Technology, Kharagpur, India. His research interests include adaptive control, robust control and control of time-delay systems. Sarit K. Das is a Professor of Electrical Engineering Department, Indian Institute of Technology, Kharagpur, India. He received the Ph.D. degree in 1985 from the same department. His research interests include design of periodic controller, decoupling of multivariable systems, modeling and robust control of complex systems. Goshaidas Ray is a Professor of Electrical Engineering Department, Indian Institute of Technology, Kharagpur, India. He received the Ph.D. degree in 1982 from Indian Institute of Technology Delhi, India. His research interests include modeling, estimation, model-based control, intelligent control, robotic systems and distributed control systems.