Geodesic
Robust controller design for linear polytopic systems
Kybernetika, Tome 42 (2006) no. 1, pp. 95-110 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 93B51, 93B52, 93C05, 93D09, 93D15, 93D21
Keywords: robust control; linear polytopic systems; output feedback; LMI approach 
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     title = {Robust controller design for linear polytopic systems},
     journal = {Kybernetika},
     pages = {95--110},
     year = {2006},
     volume = {42},
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     zbl = {1249.93138},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2006_42_1_a4/}
}
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Veselý, Vojtech. Robust controller design for linear polytopic systems. Kybernetika, Tome 42 (2006) no. 1, pp. 95-110. http://geodesic.mathdoc.fr/item/KYB_2006_42_1_a4/

[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 | MR | Zbl

[4] Boyd S., Ghaoui L. El, Feron, E., Balakrishnan V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia 1994 | MR | Zbl

[5] Chilali M., Gahinet, P., Apkarian P.: Robust pole placement in LMI region. IEEE Trans. Automat. Control 44 (1999), 12, 2257–2267 | DOI | MR

[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 | Zbl

[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 | MR | Zbl

[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

[12] Kučera V., Souza C. E. De: A necessary and sufficient conditions for output feedback stabilizability. Automatica 31 (1995), 9, 1357–1359 | DOI | MR

[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 | MR | Zbl

[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 | MR | Zbl

[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

[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

[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 | MR | Zbl