Mathematical Problems in Engineering
Volume 4 (1999), Issue 6, Pages 505-528
Controller design for bilinear systems with parametric uncertainties
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
control in which both robust stability and a prescribed
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
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.