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Article

Keywords:
robust control; parameter dependent Lyapunov function; affine quadratic stability; LMI approach
Summary:
The paper addresses the problem robust output feedback controller design with guaranteed cost and affine quadratic stability for linear continuous time affine systems. The proposed design method leads to a non-iterative LMI based algorithm. A numerical example is given to illustrate the design procedure.
References:
[1] Benton R. E., Jr., Smith D.: A non iterative LMI based algorithm for robust static output feedback stabilization. Internat. J. Control 72 (1999), 1322–1330 DOI 10.1080/002071799220290 | MR 1712166 | Zbl 0960.93048
[2] Boyd S., Ghaoui L. El., Feron, E., Balakrishnan V.: Linear Matrix Inequalities in System and Control Theory. SIAM 115 (1994), Philadelphia MR 1284712 | Zbl 0816.93004
[3] Crusius C. A. R., Trofino A.: Sufficient LMI conditions for output feedback control problems. IEEE Trans. Automat. Control 44 (1999), 5, 1053–1057 DOI 10.1109/9.763227 | MR 1690555 | Zbl 0956.93028
[4] Ghaoui L. El, Balakrishnan V.: Synthesis of fixed structure controllers via numerical optimization. In: Proc. 33rd Conference on Decision and Control, Lake Buena Vista, FL 1994, pp. 2678–2683
[5] Gahinet P., Apkarian, P., Chilali M.: Affine parameter dependent Lyapunov functions and real parametric uncertainty. IEEE Trans. Automat. Control 41 (1996), 436–442 DOI 10.1109/9.486646 | MR 1382994 | Zbl 0854.93113
[6] Gahinet P., Nemirovski A., Laub A. J., Chilali M.: LMI Control Toolbox User’s Guide. The Mathworks Inc., Natick MA 1995
[7] Geromel J. C., Souza C. E. De, Skelton R. E.: Static output feedback controllers: stability and convexity. IEEE Trans. Automat. Control 43 (1998), 120–125 DOI 10.1109/9.654912 | MR 1604277 | Zbl 0952.93106
[8] Goh K. C., Safonov M. G., Papavassilopoulos G. P.: Global optimization for the biaffine matrix inequality problem. J. Global Optim. 7 (1995), 365–380 DOI 10.1007/BF01099648 | MR 1365801 | Zbl 0844.90083
[9] Gyurkovics E., Takacs T.: Stabilisation of discrete-time interconnected systems under control constraints. Proc. IEE Control Theory and Applications 147 (2000), 137–144
[10] Hejdiš J., Kozák, Š., Juráčková L.: Self-tuning controllers based on orthonormal functions. Kybernetika 36 (2000), 477–491
[11] Henrion D., Alzelier, D., Peaucelle D.: Positive polynomial matrices and improved robustness conditions. In: Proc. 15th Triennial World Congres, Barcelona 2002, CD
[12] Kose I. E., Jabbari F.: Robust control of linear systems with real parametric uncertainty. Automatica 35 (1999), 679–687 DOI 10.1016/S0005-1098(98)00184-8 | MR 1827393 | Zbl 0982.93033
[13] A.Kozáková: Robust Decentralized control of complex systems in frequency domain. In: Preprints of 2nd IFAC Workshop on NTDCS, Elsevier Kidlington UK, 1999
[14] Kučera V., Souza C. E. De: A necessary and sufficient conditions for output feedback stabilizability. Automatica 31 (1995), 1357–1359 DOI 10.1016/0005-1098(95)00048-2 | MR 1349414
[15] Yu, Li, Chu, Jian: An LMI approach to guaranteed cost of linear uncertain time delay systems. Automatica 35 (1999), 1155–1159 DOI 10.1016/S0005-1098(99)00007-2 | MR 1831625
[16] Mehdi D., Hamid, M. Al, Perrin F.: Robustness and optimality of linear quadratic controller for uncertain systems. Automatica 32 (1996), 1081–1083 DOI 10.1016/0005-1098(96)00037-4 | MR 1405468 | Zbl 0855.49024
[17] 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
[18] Pakshin P. V.: Robust decentralized control of systems of random structure. J. Computer and Systems Sciences 42 (2003), 200–204 MR 2000651 | Zbl 1110.93300
[19] Park P., Moon Y. S., Kwon W. H.: A stabilizing output feedback linear quadratic control for pure input delayed systems. Internat. J. Control 72 (1999), 385–391 DOI 10.1080/002071799221019 | MR 1674930 | Zbl 0956.93053
[20] Takahashi R. H. C., Ramos D. C. W., Peres P. L. D.: Robust control synthesis via a genetic algorithm and LMIS. In: Preprints 15th Triennial World Congress, Barcelona 2002, CD
[21] Tuan H. D., Apkarian P., Hosoe, S., Tuy H.: D. C. optimization approach to robust control: feasibility problems. Internat. J. Control 73 (2000), 89–104 DOI 10.1080/002071700219803 | MR 1738361 | Zbl 0998.93012
[22] Veselý V.: Static output feedback controller design. Kybernetika 37 (2001), 205–221 MR 1839228
[23] Veselý V.: Robust output feedback controller design for linear parametric uncertain systems. J. Electrical Engineering 53 (2002), 117–125
[24] Xu S. J., Darouch M.: On the robustness of linear systems with nonlinear uncertain parameters. Automatica 34 (1998), 1005–1008 DOI 10.1016/S0005-1098(98)00040-5 | MR 1823000
[25] Cao, Yong Yan, Sun, You Xian: Static output feedback simultaneous stabilization: LMI approach. Internat. J. Control 70 (1998), 803–814 DOI 10.1080/002071798222145 | MR 1634668
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