Abstract
Multi-objective robust state-feedback controller synthesis problems for linear discrete-time uncertain systems are addressed. Based on parameter-dependent Lyapunov functions, the Gl 2 and GH 2 norm expressed in terms of LMI (Linear Matrix Inequality) characterizations are further generalized to cope with the robust analysis for convex polytopic uncertain system. Robust state-feedback controller synthesis conditions are also derived for this class of uncertain systems. Using the above results, multi-objective state-feedback controller synthesis procedures which involve the LMI optimization technique are developed and less conservative than the existing one. An illustrative example verified the validity of the approach.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D’Andrea, R., 1999. Generalizedl 2 synthesis.IEEE Tran. on Automatic Control,44: 1145–1156.
de Oliverira, M.C., Bernussou, J., Geromel, J.C., 1999a. A new discrete time robust stability condition.Systems and Control Letters,37: 261–265.
de Oliverira, M.C., Geromel, J.C., Bernussou, J., 1999b. An LMI Optimization Approach to Multiobjective Controller Design for Discrete-time Systems. Proceedings of the 38th Conference on Decision and Control. Phoenix, Arizona, p. 3611–3616.
de Oliverira, M.C., Geromel, J.C., Bernussou, J., 2002. ExtendedH2 andH ∞ norm characterization and controller parameterization for discrete-time systems.International Journal of Control,75(9): 666–679.
Mibar, H., Kochbatt, A., Zaafouri, A., Ksouri, M., 2002. An LMI Approach toH2/H ∞ Synthesis for Polytopic Uncertain Systems. IEEE International Conference on Systems, Man and Cybernetics.
Scherer, C., Gahinet, P., Chilali, M., 1997. Multiobjective output feedback control via LMI optimization.IEEE Tran. on Automatic Control. 42: 896–911.
Wang, J., Wilson, D.A., 2001. Mixed Gl 2/H 2/GH 2 control with pole placement and its application to vehicle suspension systems.International Journal of Control,74: 1353–1369.
Yan, W.J., Zhang, S.L., 2004. Mixed Gl 2/GH 2 multi-channel multi-objective control synthesis for discrete time systems.Journal of Zhejiang University SCIENCE,5(7): 827–834.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project (No. 60374028) supported by the National Natural Science Foundation of China
Rights and permissions
About this article
Cite this article
Zhang, Yh., Yan, Wj., Lu, Jn. et al. Multi-objective robust controller synthesis for discrete-time systems with convex polytopic uncertain domain. J. Zheijang Univ.-Sci. 6 (Suppl 1), 87–93 (2005). https://doi.org/10.1631/jzus.2005.AS0087
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/jzus.2005.AS0087
Key words
- Gl 2 and GH 2 performance
- Multi-objective optimization
- Robust controller synthesis
- Parameter-dependent Lyapunov functions
- Convex polytopic uncertain system