Mathematical Problems in Engineering
Volume 4 (1999), Issue 6, Pages 505-528

Controller design for bilinear systems with parametric uncertainties

Peng Shi,1 Shyh-Pyng Shue,2 Yan Shi,3 and Ramesh K. Agarwal2

1Centre for Industrial & Applicable Mathematics, School of Mathematics, The University of South Australia, The Levels, SA 5095, Australia
2National Institute for Aviation Research, Department of Aerospace Engineering, Wichita State University, Wichita 67260, KS, USA
3School of Engineering, Kyushu Tokai University, 9-1-1, Toroku, Kumamoto 862-8652, Japan

Received 11 September 1997; Revised 13 May 1998

Copyright © 1999 Peng Shi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper studies the problem of robust control of a class of uncertain bilinear continuous-time systems. The class of uncertain systems is described by a state space model with time-varying norm-bounded parameter uncertainty in the state equation. We address the problem of robust H control in which both robust stability and a prescribed H performance are required to be achieved irrespective of the uncertainties. Both state feedback and output feedback controllers are designed. It has been shown that the above problems can be recast into H syntheses for related bilinear systems without parameter uncertainty, which can be solved via a Riccati inequality approach. Two examples are given to show the potential of the proposed technique.