Article
Full entry |
PDF
(0.8 MB)
Feedback
PDF
(0.8 MB)
Feedback
Keywords:
decentralized control; descriptor systems; parametric uncertainty; homotopy method; nonlinear matrix inequality
decentralized control; descriptor systems; parametric uncertainty; homotopy method; nonlinear matrix inequality
Summary:
This paper considers a robust decentralized $H_2$ control problem for multi-channel descriptor systems. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in both the system and control input matrices. Our interest is focused on dynamic output feedback. A necessary and sufficient condition for an uncertain multi-channel descriptor system to be robustly stabilizable with a specified $H_2$ norm is derived in terms of a strict nonlinear matrix inequality (NMI), that is, an NMI with no equality constraint. A two-stage homotopy method is proposed to solve the NMI iteratively. First, a decentralized controller for the nominal descriptor system is computed by imposing block-diagonal constraints on the coefficient matrices of the controller gradually. Then, the decentralized controller is modified, again gradually, to cope with the uncertainties. On each stage, groups of variables are fixed alternately at the iterations to reduce the NMI to linear matrix inequalities (LMIs). An example is given to show the efficiency of this method.
References:
[1] J. H. Alva: The feasibility of continuation methods for nonlinear equations. SIAM J. Numer. Anal. 11 (1974), 1, 102–120. MR 0418448
[2] T. N. Chang and E. J. Davison: Decentralized control of descriptor systems. IEEE Trans. Automat. Control 46 (2001), 1589–1595. MR 1858060
[3] N. Chen, M. Ikeda, and W. Gui: Robust decentralized $H_\infty $ control of interconnected systems: A design method using homotopy. In: Preprints 10th IFAC/IFORS/IMACS/IFIP Symposium on Large Scale Systems: Theory and Applications, Osaka 2004, pp. 330–336.
[4] L. Dai: Singular Control Systems. Springer-Verlag, Berlin 1989. MR 0986970 | Zbl 0669.93034
[5] M. Ikeda, T. W. Lee, and E. Uezato: A strict LMI condition for $H_2$ control of descriptor systems. In: Proc. 39th IEEE Conference on Decision and Control 2000, pp. 601–604.
[6] M. Ikeda, G. Zhai, and E. Uezato: Centralized design of decentralized stabilizing controllers for large-scale descriptor systems. DCDIS Journal, Series B: Algorithms and Applications 11 (2004), 509–520. MR 2071224
[7] I. Masubuchi, Y. Kamitane, A. Ohara, and N. Suda: $H_\infty $ control for descriptor systems: A matrix inequalities approach. Automatica 33 (1997), 669–673. MR 1448959
[8] I. R. Petersen: A stabilization algorithm for a class of uncertain linear systems. Systems Control Lett. 8 (1987), 351–357. MR 0884885 | Zbl 0648.93042
[9] K. Takaba: $H_2$ output feedback control for descriptor systems. Automatica 34 (1998), 7, 841–850. MR 1635088 | Zbl 0961.93012
[10] D. Wang and P. Bao: Robust impulse of uncertain singular systems by decentralized output feedback. IEEE Trans. Automat. Control 45 (2000), 500–505. MR 1762865
[11] D. Wang and C. B. Soh: On regularizing singular systems by decentralized output feedback. IEEE Trans. Automat. Control 44 (1999), 148–152. MR 1666924
[12] S. L. Wo and Y. Zou: Decentralized robust stabilization for singular large scale systems with parameter uncertainty. Control and Decision 19 (2004), 8, 931–934 (in Chinese). MR 2079743
[13] H. S. Yang, Q. L. Zhang, and C. M. Shang: $H_2$ optimal control for descriptor systems. Acta Automat. Sinica 28 (2002), 6, 920–926 (in Chinese).
[14]
R. Yu and D. Wang. (2003). On impulsive modes of linear singular systems subject to decentralized output feedback. IEEE Trans. Automat. Control 48 (2003), 1804–1809. MR 2021433
[15] G. Zhai, M. Ikeda, and Y. Fujisaki: Decentralized $H_\infty $ controller design: A matrix inequality approach using a homotopy method. Automatica 37 (2001), 4, 565–573. MR 1832530
[16] G. Zhai, M. Yoshida, J. Imae, and T. Kobayashi: Decentralized $H_2$ controller design for descriptor systems: An LMI approach. Nonlinear Dynamics and Systems Theory 6 (2006), 1, 98–108. MR 2222782
Search
Partner of
