Abstract
A bilinear observer is proposed for a class of singular bilinear system subject to unknown input disturbance. Based on singular value decomposition technique, the existence of the solution to the decomposed system is presented. Then a bilinear observer is proposed for the decomposed system based on an algebraic Riccati equation, and the domain of attraction of the state estimation error is derived. Finally, a detailed design procedure is given to design a bilinear observer for a model of flexible joint robot, which demonstrates the effectiveness of the proposed method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. C. Kantor. A finite dimensional nonlinear observer for an exothermic stirred-tank reactor[J]. Chemical Engineering Science, 1989, 44(11): 1503–1509.
F. E. Thau. Observing the state of nonlinear dynamic systems[J]. Int. J. of Control, 1973, 17(3): 471–478.
S. K. Zak. On the stabilization and observation of nonlinear and uncertain dynamic systems[J]. IEEE Trans. on Automatic Control, 1990, 35(3): 604–607.
E. A. Garcia, P. M. Frank. Deterministic nonlinear observer-based approaches to fault diagnosis: a survey[J]. Control Engineering and Practices, 1997, 5(5): 663–670.
H. Shim, J. H. Seo, A. R. Teel. Nonlinear observer design via passivation of error dynamics[J]. Automatica, 2003, 39(7): 885–892.
D. Yu, D. N. Shield. A bilinear observer fault detection observer[J]. Automatica, 1996, 32(11): 1597–1602.
F. L. Lewis. A survey of linear singular systems[J]. Circuits, Systems and Signal Processing, 1986, 5(1): 3–36.
Q. Zhang, D. Yang. Analysis and Synthesis for Uncertain Descriptor Systems[M]. Shenyang: Press of Northeastern University, 2003: 58–67.
D. N. Shield. Observer design and detection for nonlinear descriptor systems[J]. Int. J. of Control, 1997, 67(2): 153–168.
D. N. Shield. Observers for descriptor systems[J]. Int. J. of Control, 1991, 55(1): 249–256.
S. Raghavar, J. K. Hedrick. Observer design for a class of nonlinear systems[J]. Int. J. of Control, 1994, 59(2): 515–528.
Author information
Authors and Affiliations
Additional information
This work was supported by the National Natural Science Foundation of China (No.60244017, 60325311).
Zhanshan WANG was born in Liaoning in 1971. He received the M.S. degree in control theory and control engineering from Fushun Petroleum Institute in 2001. He is now a lecturer in Shenyang Ligong University and pursuing the Ph.D. degree in Northeastern University. His research interests are in fault diagnosis, fault tolerant control and stability of recurrent neural networks.
Huaguang ZHANG was born in Jilin in 1959. He received the Ph.D. degree from Southeastern University in 1991. Now he is a professor in Northeastern University. His research interests include fuzzy control, process control, nonlinear control and dynamics of recurrent neural networks.
Rights and permissions
About this article
Cite this article
Wang, Z., Zhang, H. Design of bilinear observer for singular bilinear systems. J. Control Theory Appl. 4, 413–417 (2006). https://doi.org/10.1007/s11768-006-4128-1
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s11768-006-4128-1