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$H _{\infty}$-control of linear state-delay descriptor systems: An LMI approach. (English) Zbl 1006.93021
The $H^\infty$ control of the linear state-delay descriptor system $$\align E\dot x(t) & =\sum^2_{i=0} A_ix(t-h_i)+ \int^0_{-d}A_dx(t+s) ds+B_1w(t)\\ x(t) & = 0,\ t\le 0\\ z(t) & =\text{col} \bigl\{C_0x(t),C_1x(t-h_1), C_2x(t-h_2)\bigr\} \endalign$$ is studied, and a delay-dependent robust controller without impulsive solutions is obtained. The method is based on the standard use of linear matrix inequalities.

93C23Systems governed by functional-differential equations
34A09Implicit equations, differential-algebraic equations
15A39Linear inequalities of matrices
Full Text: DOI
[1] T. Azuma, K. Ikeda, K. Uchida, Infinite-dimensional LMI approach to H\infty-control synthesis for linear systems with time delay, in: Proceedings of the 5th European Control Conference, Karlsruhe, Germany, September 1999
[2] A. Bensoussan, G. DoPrato, M.C. Delfour, S.K. Mitter, Representation and control of infinite dimensional systems, vol. 1--2, Birkhäser, Basel, 1992
[3] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V.: Linear matrix inequality in systems and control theory. SIAM frontier series (April 1994) · Zbl 0816.93004
[4] Brayton, R.: Small signal stability criterion for electrical networks containing lossless transmission lines. IBM J. Res. develop. 12, 431-440 (1968) · Zbl 0172.20703
[5] Bunse-Gerstner, A.; Byers, R.; Mehrmann, V.; Nickols, N.: Feedback design for regularizing descriptor systems. Linear algebra appl. 299, 119-151 (1999) · Zbl 0944.65082
[6] Campbell, S.: Singular linear systems of differential equations with delays. Appl. anal. 2, 129-136 (1980) · Zbl 0444.34062
[7] S. Campbell, 2-D (differential-delay) implicit systems, in: Proceedings of IMACS World Congress on Scientific Computation, Dublin, 1991, pp. 1828--1829
[8] Dai, L.: Singular control systems. (1989) · Zbl 0669.93034
[9] Fridman, E.: New Lyapunov--Krasovskiĭ functionals for stability of linear retarded and neutral type systems. Systems control lett. 43, No. 4, 309-319 (2001) · Zbl 0974.93028
[10] E. Fridman, Stability of linear descriptor systems with delay: a Lyapunov-based approach, J. Math. Anal. Appl. (under review) · Zbl 1032.34069
[11] Fridman, E.; Shaked, U.: H\infty-state-feedback control of linear systems with small state-delay. Systems control lett. 33, 141-150 (1998) · Zbl 0902.93022
[12] E. Fridman, U. Shaked, A descriptor system approach to H\infty control of linear time-delay systems, IEEE Trans. Automat. Control 47 (2002)
[13] Halanay, A.; Rasvan, V.: Stability radii for some propagation models. IMA J. Math. control inform. 14, 95-107 (1997) · Zbl 0873.93067
[14] Hale, J.; Lunel, S.: Introduction to functional differential equations. (1993) · Zbl 0787.34002
[15] Hale, J.; Amores, P. Martinez: Stability in neutral equations. J. nonlinear anal. Theory, meth. Appl. 1, 161-172 (1977) · Zbl 0359.34070
[16] Ivanescu, D.; Dion, J-M.; Dugard, L.; Niculescu, S. I.: Dynamical compensation for time-delay systems: an LMI approach. Internat. J. Robust nonlinear control 10, 611-628 (2000) · Zbl 0963.93073
[17] Kolmanovskii, V.; Myshkis, A.: Applied theory of functional differential equations. (1999) · Zbl 0917.34001
[18] Kolmanovskii, V.; Niculescu, S. I.; Richard, J. P.: On the Liapunov--Krasovskiĭ functionals for stability analysis of linear delay systems. Internat. J. Control 72, 374-384 (1999) · Zbl 0952.34057
[19] Kwakernaak, H.: Frequency domain solution of the H$\infty $problem for descriptor systems. Lecture notes in control and information sciences 241, 317-336 (1999)
[20] Logemann, H.: Destabilizing effects of small time delays on feedback-controlled descriptor systems. Linear algebra appl. 272, 131-153 (1998) · Zbl 0986.93056
[21] Masubuchu, I.; Kamitane, Y.; Ohara, A.; Suda, N.: H$\infty $control for descriptor systems: a matrix inequalities approach. Automatica 33, 669-673 (1997) · Zbl 0881.93024
[22] S.-I. Niculescu, V. Rasvan, Delay-independent stability in lossless propagation models with applications, in: Proceedings of MTNS 2000, Perpignan, France, 2000
[23] V. Rasvan, Absolute Stability of Time Lag Control Systems, Ed. Academiei, Bucharest, 1975 (in Romanian) · Zbl 0312.93029
[24] De Souza, C. E.; Li, X.: Delay-dependent robust H$\infty $control of uncertain linear state-delayed systems. Automatica 35, 1313-1321 (1999) · Zbl 1041.93515
[25] Park, P.: A delay-dependent stability criterion for systems with uncertain time-invariant delays. IEEE trans. Automat. control 44, 876-877 (1999) · Zbl 0957.34069
[26] A. Rehm, F. Allgower, Descriptor and nondescriptor controllers in H\infty control of descriptor systems, in: Proceedings of ROCOND, Prague, 2000
[27] Takaba, K.; Morihira, N.; Katayama, T.: H$\infty $control for descriptor systems--a J-spectral factorization approach. Proceedings of the 33rd IEEE conf. Decision and control, 2251-2256 (1994)
[28] Zhu, W.; Pitzold, L.: Asymptotic stability of linear delay differential--algebraic equations and numerical methods. Appl. numer. Math. 24, 247-264 (1997) · Zbl 0879.65060
[29] Xu, H.; Mizukami, K.: Upper and lower bounds of h\infty-optimal performance for a class of continuous type descriptor systems. Proceedings of the 38th conf. Decision and control, cobe, Japan 1, 1021-1026 (1996)