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decentralized control; large scale complex systems; nonlinear systems; continuous-time systems; delay; reduced-order systems
The paper deals with the synthesis of a non-fragile state controller with reduced design complexity for a class of continuous-time nonlinear delayed symmetric composite systems. Additive controller gain perturbations are considered. Both subsystems and interconnections include time-delays. A low-order control design system is first constructed. Then, stabilizing controllers with norm bounded gain uncertainties are designed for the control design system using linear matrix inequalities (LMIs) for both delay-independent and delay-dependent stability approaches. The main result shows that when such a non-fragile low-order controllers are implemented into each local controller of the decentralized controller for the global system, the global closed-loop systems are globally asymptotically stable.
[1] L. Bakule: Decentralized control of time-delayed uncertain symmetric composite systems. In: Proc. 4th International Conference on Control and Automation, Montreal 2003, pp. 399–403.
[2] L. Bakule: Control of time-delayed uncertain symmetrically coupled systems. In: Proc. 6th IASTED Internat. Conference Intelligent Systems and Control, Acta Press, Honolulu 2004, pp. 156–160.
[3] L. Bakule: Complexity-reduced guaranteed cost control design for delayed uncertain symmetrically connected systems. In: Proc. American Control Conference, Portland 2005, pp. 2590–2595.
[4] L. Bakule: Resilient stabilization of uncertain state-delayed symmetric composite systems. In: Proc. 25th IASTED International Conference on Modelling, Identification, and Control, Acta Press, Lanzarote 2006, pp. 149–154.
[5] L. Bakule: Non-fragile controllers for a class of time-delay nonlinear systems. In: Prepr. 11th IFAC/IFORS/IMACS Symposium on Large Scale Systems: Theory and Applications, Gdansk 2007. Zbl 1158.93302
[6] L. Bakule and J. Lunze: Decentralized design of feedback control for large-scale systems. Kybernetika 24 (1988), 1–100. MR 0975855
[7] L. Bakule and J. Rodellar: Decentralized control design of uncertain nominally linear symmetric composite systems. IEE Proc. Control Theory Appl. 143 (1996), 630–536.
[8] L. Bakule and M. De la Sen: Decentralized stabilization of uncertain symmetric composite systems. In: Proc. 9th IFAC/IFORS/IMACS Symposium on Large Scale Systems: Theory and Applications, Patras 1998, vol. 1, pp. 265–270.
[9] S. P. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia 1994. MR 1284712
[10] J. R. Corrado and W. M. Haddad: Static output feedback controllers for systems with parametric uncertainty and controller gain variations. In: Proc. American Control Conference, San Diego 1999, pp. 915–919.
[11] P. Dorado: Non-fragile controller design: an overview. In: Proc. American Control Conference, Philadelphia 1998, pp. 2829–2831.
[12] W. Ebert: Towards delta domain in predictive control – An application to the space crystal furnace TITUS. In: Proc. 1999 Internat. Conference on Control Applications, Banff 1999, pp. 391–396.
[13] M. El-Sayed and P. S. Krishnaprasad: Homogeneous interconnected systems: An example. IEEE Trans. Automat. Control 26 (1981), 894–901.
[14] M. Hovd and S. Skogestad: Control of symetrically interconnected plants. Automatica 30 (1994), 957–973. MR 1283439
[15] S. Huang, J. Lam, G. H. Yang, and S. Zhang: Fault tolerant decentralized $H_{\infty }$ control for symmetric composite systems. IEEE Trans. Automat. Control 44 (1999), 2108–2114. MR 1735725
[16] R. S. H. Istepanian and J. F. Whidborne (eds.): Digital Controller Implementation and Fragility. Springer-Verlag, Berlin 2001.
[17] L. H. Keel and S. P. Bhattacharyya: Robust, fragile, or optimal? IEEE Trans. Automat. Control 42 (1997), 1098–1105. MR 1469070
[18] F. Liu, P. Jiang, H. Su, and J. Chu: Robust ${H}_{\infty }$ control for time-delay systems with additive controller uncertainty. In: Proc. 4th World Congress on Intelligent Control and Automation, 2002, pp. 1718–1722.
[19] F. Liu and S. Y. Zhang: Robust decentralized output feedback control of similar composite systems with uncertainties unknown. In: Proc. American Control Conference, San Diego 1999, vol. 6, pp. 3838–3842.
[20] M. S. Mahmoud: Resilient Control of Uncertain Dynamical Systems. Springer Verlag, Berlin 2004. MR 2073581 | Zbl 1103.93003
[21] J. A. Marshall, M. E. Broucke, and B. A. Francis: Formations of vehicles in cyclic pursuit. IEEE Trans. Automat. Control 49 (2004), 1963–1974. MR 2100774
[22] D. Peaucelle, D. Arzelier, and Ch. Farges: LMI results for resilient state-feedback with ${H}_{\infty }$ performance. In: Proc. 43rd IEEE Conference on Decision and Control, Paradise 2004, pp. 400–405.
[23] S. S. Stanković, D. M. Stipanović, and D. D. Šiljak: Decentralized dynamic output feedback for robust stabilization of a class of nonlinear interconnected systems. Automatica 43 (2007), 861–867.
[24] D. D. Šiljak and D. M. Stipanović: Robust stabilization of nonlinear systems: The LMI approach. Math. Problems Engrg. 6 (2000), 461–493.
[25] R. H. C. Takahashi, D. A. Dutra, R. M. Palhares, and P. L. D. Peres: On robust non-fragile static state-feedback controller synthesis. In: Proc. 39th IEEE Conference on Decision and Control, Sydney 2000, pp. 4909–4914.
[26] A. Trächtler: Entwurf strukturbeschränkter Rückführungen an symmetrischen Systemen. Automatisierungstechnik 39 (1991), 239–244.
[27] M. Vukobratović and D. M. Stokić: Control of Manipulator Robots: Theory and Applications. Springer-Verlag, Berlin 1982.
[28] Y. H. Wang and S. Y. Zhang: Robust control for nonlinear similar composite systems with uncertain parameters. IEE Proc. Control Theory Appl. 147 (2000), 80–84.
[29] L. Xiaoping: Output regulation of strongly coupled symmetric composite systems. Automatica 28 (1992), 1037–1041. MR 1179706 | Zbl 0766.93027
[30] G.-H. Yang and J. L. Wang: Non-fragile ${H}_{\infty }$ control for linear systems with multiplicative controller gain variations. Automatica 37 (2001), 727–737. MR 1832962
[31] G. H. Yang and S. Y. Zhang: Stabilizing controllers for uncertain symmetric composite systems. Automatica 31 (1995), 337–340. MR 1315147
[32] G. H. Yang and S. Y. Zhang: Robust stability and stabilization of uncertain composite systems with circulant structures. In: Proc. 13th Triennial World Congress, San Francisco 1996, 5a-02 6, pp. 67–72. MR 1423662
[33] J.-S. Yee, G.-H. Wang, and J. L. Wang: Non-fragile guaranteed cost control for discrete-time uncertain linear systems. Internat. J. Systems Sci. 63 (2001), 7, 845–853. MR 1959615
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