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Abstract: Based on input-output approach, the robust stability and stabilization problems for uncertain singular systems with time-varying delays are investigated. The parameter uncertainties are assumed to be norm-bounded and the time-varying delays include both discrete delay and distributed delay. By introducing a new input-output model, the time-delay system is embedded in a family of systems with a forward system without time delay and a dynamical feedback uncertainty. A sufficient and necessary condition, which guarantees the system regular, impulse-free and stable for all admissible uncertainties, is obtained. Based on the strict linear matrix inequality, the desired robust state feedback controller is also obtained. Finally, a numerical example is provided to demonstrate the application of the proposed method.

[1] Bliman, P.A., 2000. Extension of Popov absolute stability criterion to non-autonomous systems with delays. Int. J. Control, 73:1349-1361.

[2] Cao, Y., Sun, Y., Lam, J., 1998. Delay dependent robust H₍ control for uncertain systems with time-varying delays. IEE Proc.-Control Theory & Appl., 145:338-344.

[3] Dai, L., 1989. Singular Control Systems. Springer-Verlag, Berlin, Germany.

[4] Desoer, C.A., Vidyasagar, M., 1975. Feedback Systems: Input-Output Properties. Academic Press, New York.

[5] Fridman, E., Shaked, U., 2006. Input-output approach to stability and L₁-gain analysis of systems with time-varying delays. Syst. & Control Lett., 55:1041-1053.

[6] Gu, K., Kharitonov, V.L., Chen, J., 2003. Stability of Time-Delay Systems. Birkhauser, Boston, p.275-323.

[7] Huang, Y.P., Zhou, K., 2000. Robust stability of uncertain time-delay systems. IEEE Trans. on Automatic Control, 45:2169-2173.

[8] Lewis, F.L., 1986. A survey of linear singular systems. Circuits, Systems & Signal Processing, 5:3-36.

[9] Ma, B., Zhu, X., Sun, J., 2005. Guaranteed cost control of uncertain T-S fuzzy descriptor systems. Proc. Int. Conf. on Machine Learning and Cybernetics, 2:742-746.

[10] Mahmoud, M., 2000. Robust Control and Filtering for Time-Delay Systems. Marcel Decker, New York.

[11] Masubuchi, I., Kamitane, Y., Ohara, A., Suda, N., 1997. H₍ control for descriptor systems: a matrix inequality approach. Automatica, 33:669-673.

[12] Niculoscu, S.I., 2001. Delay Effects on Stability—A Robust Control Approach. Springer-Verlag, London.

[13] Petersen, I.R., 1987. A stabilization algorithm for a class of uncertain linear systems. Syst. & Control Lett., 8:351-357.

[14] Vidyasagar, M., 1993. Nonlinear Systems Analysis (2nd Ed.). Prentice-Hall, Englewood Cliffs, NJ.

[15] Wang, H., Xue, A., Lu, R., Xu, Z., Wang, J., 2007. Robust H₍ control for discrete singular systems with parameter uncertainties. Acta Automatica Sinica, 33:1300-1305 (in Chinese).

[16] Xu, S., Dooren, P.V., Stefan, R., Lam, J., 2002. Robust stability and stabilization for singular systems with state delay and parameter uncertainty. IEEE Trans. on Automatic Control, 47:1122-1128.

[17] Xu, S., Lam, J., Liu, W., Zhang, Q., 2003a. H₍ model reduction for singular systems: continuous-time case. IEE Proc.-Control Theory & Appl., 150:637-641.

[18] Xu, S., Lam, J., Yang, C., 2003b. Robust H₍ control for uncertain singular systems with state delay. Int. J. Rob. Nonl. Control, 13:1213-1223.

[19] Yue, D., Han, Q.L., 2005. Delay-dependent robust H₍ controller design for uncertain descriptor systems with time-varying discrete and distributed delays. IEE Proc.-Control Theory & Appl., 152:628-638.

[20] Zhou, S., Lam, L., 2003. Robust stabilization of delayed singular systems with linear fractional parametric uncertainties. Circuits, Systems & Signal Processing, 22:579-588.