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robust control; linear polytopic systems; output feedback; LMI approach
The paper addresses the problem of the robust output feedback controller design with a guaranteed cost and parameter dependent Lyapunov function for linear continuous time polytopic systems. Two design methods based on improved robust stability conditions are proposed. Numerical examples are given to illustrate the effectiveness of the proposed methods. The obtained results are compared with other three design procedures.
[1] Apkarian P., Feron, E., Gahinet P.: Parameter-dependent Lyapunov functions for robust control of systems with real parametric uncertainty. In: Proc. 3rd EEC, Rome 1995, pp. 2275–2280
[2] Bachelier O., Bernussou J., Oliveira M. C. de, Geromel J. C.: Parameter dependent Lyapunov control design: Numerical evaluation. In: Proc. 38th Conference on DC, Phoenix 1999, Arizona, pp. 293–297
[3] Jr. R. J. Benton, Smith D.: A non iterative LMI based algorithm for robust static output feedback stabilization. Internat. J. Control 72 (1999), 14, 1322–1330 DOI 10.1080/002071799220290 | MR 1712166 | Zbl 0960.93048
[4] Boyd S., Ghaoui L. El, Feron, E., Balakrishnan V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia 1994 MR 1284712 | Zbl 0816.93004
[5] Chilali M., Gahinet, P., Apkarian P.: Robust pole placement in LMI region. IEEE Trans. Automat. Control 44 (1999), 12, 2257–2267 DOI 10.1109/9.811208 | MR 1728961
[6] Dettori M., Scherer W. C.: New robust stability and performance conditions based on parameter dependent multiplier. In: Proc. 39th IEEE Conference on Decision and Control, Sydney 2000, CD-ROM
[7] Gahinet P., Apkarian, P., Chilali M.: Affine parameter-dependent Lyapunov functions and real parametric uncertainty. IEEE Trans. Circuits and Systems 41 (1996), 3, 436–442 MR 1382994 | Zbl 0854.93113
[8] Grman L., Rosinová D., Kozáková, A., Veselý V.: Robust stability conditions for polytopic systems. Internat. J. System Sci. 36 (2005), 15, 961–973 DOI 10.1080/00207720500389592 | MR 2192005 | Zbl 1126.93409
[9] Han J., Skelton R. E.: An LMI optimization approach for structured linear controllers. In: Proc. 42th IEEE Conference on Decision and Control, Maui 2003, pp. 5143–5148
[10] Henrion D., Alzelier, D., Peaucelle D.: Positive polynomial matrices and improved robustness conditions. In: 15th Triennial World Congress of the International Federation of Automatic Control, Barcelona 2002, CD-ROM
[11] Henrion D., Sagimoto,, Kenji, Šebek M.: Rank-one LMI approach to robust stability of polynomial matrices. Kybernetika 38 (2002), 5, 643–656 MR 1966952
[12] Kučera V., Souza C. E. De: A necessary and sufficient conditions for output feedback stabilizability. Automatica 31 (1995), 9, 1357–1359 DOI 10.1016/0005-1098(95)00048-2 | MR 1349414
[13] Oliveira M. C. de, Bernussou, J., Geromel J. C.: A new discrete–time robust stability condition. Systems Control Lett. 37 (1999), 261–265 DOI 10.1016/S0167-6911(99)00035-3 | MR 1751256 | Zbl 0948.93058
[14] Oliveira M. C. de, Camino J. F., Skelton R. E.: A convexifying algorithm for the design of structured linear controllers. In: Proc. 39th IEEE Conference on Decision and Control, Sydney 2000, pp. 2781–2786
[15] Peaucelle D., Arzelier D., Bachelier O., Bernussou J.: A new robust D-stability condition for real convex polytopic uncertainty. Systems Control Lett. 40 (2000), 21–30 DOI 10.1016/S0167-6911(99)00119-X | MR 1829071 | Zbl 0977.93067
[16] Rosinová D., Veselý V.: Robust output feedback design of linear discrete–time systems: LMI Approach. In: 4th IFAC Symposium on Robust Control Design, Milano 2003, CD-ROM
[17] Skelton R. E., Iwasaki, T., Grigoriadis K.: A Unified Algebraic Approach to Linear Control Design. Taylor and Francis, London 1998 MR 1484416
[18] Takahashi R. H. C., Ramos D. C. W., Peres P. L. D.: Robust control synthesis via a genetic algorithm and LMI’s. In: 15th Triennial World Congress of the International Federation of Automatic Control, Barcelona 2002, CD-ROM
[19] Veselý V.: Static output feedback controller design. Kybernetika 37 (2001), 2, 205–221 MR 1839228
[20] Veselý V.: Robust output feedback control synthesis: LMI approach. In: 3rd IFAC Conference on Control System Design, Bratislava 2003, CD-ROM
[21] Cao, Yong Yan, Sun, You Xian: Static Output feedback simultaneous stabilization. LMI approach. Internat. J. Control 70 (1998), 5, 803–814 DOI 10.1080/002071798222145 | MR 1634668 | Zbl 0930.93066
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