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Robust sampled-data stabilization of linear systems: an input delay approach. (English) Zbl 1072.93018
The authors develop necessary LMI conditions for checking whether a linear static state feedback asymptotically stabilizes a linear sampled-data system with known bound on the sampling rate. The results are obtained by interpreting sampling as a time-varying uncertain delay and by representing the resulting system in descriptor form. The LMIs are show to be feasible for continuous-time stabilizing controllers under sufficiently fast sampling. Extensions to saturated feedback laws are also discussed.

93C57Sampled-data control systems
93D15Stabilization of systems by feedback
93C05Linear control systems
15A39Linear inequalities of matrices
34A09Implicit equations, differential-algebraic equations
Full Text: DOI
[1] Astrom, K.; Wittenmark, B.: Adaptive control. (1989)
[2] Bamieh, B.; Pearson, J.; Francis, B.; Tannenbaum, A.: A lifting technique for linear periodic systems. Systems and control letters 17, 79-88 (1991) · Zbl 0747.93057
[3] Basar, T., & Bernard, P. (1995). H\inftyoptimal control and related minimax design problems. A dynamic game approach. Systems and control: Foundation and applications. Boston: Birkhauser.
[4] Cao, Y.; Lin, Z.; Hu, T.: Stability analysis of linear time-delay systems subject to input saturation. IEEE transactions on circuits and systems 49, 233-240 (2002)
[5] Cao, Y.; Sun, Y.; Cheng, C.: Delay-dependent robust stabilization of uncertain systems with multiple state delays. IEEE transactions on automatic control 43, 1608-1612 (1998) · Zbl 0973.93043
[6] Chen, T.; Francis, B.: H2 optimal sampled-data control. IEEE transactions on automatic control 36, 387-397 (1991) · Zbl 0748.93063
[7] Dullerud, G.; Glover, K.: Robust stabilization of sampled-data systems to structured LTI perturbations. IEEE transactions on automatic control 38, 1497-1508 (1993) · Zbl 0790.93111
[8] Fridman, E.: Use of models with aftereffect in the problem of design of optimal digital control. Automation and remote control 53, No. 10, 1523-1528 (1992)
[9] Fridman, E.: Stability of linear descriptor systems with delaya Lyapunov-based approach. Journal of mathematical analysis and applications 273, No. 1, 24-44 (2002) · Zbl 1032.34069
[10] Fridman, E.; Pila, A.; Shaked, U.: Regional stabilization and H$\infty $control of time-delay systems with saturating actuators. International journal of robust and nonlinear control 13, No. 9, 885-907 (2003) · Zbl 1029.93022
[11] Fridman, E.; Shaked, U.: An improved stabilization method for linear time-delay systems. IEEE transactions on automatic control 47, No. 11, 1931-1937 (2002)
[12] Gao, H.; Wang, C.: Comments and further results on a ”descriptor system approach to H$\infty $control of linear time-delay systems”. IEEE transactions on automatic control 48, No. 3, 520-525 (2003)
[13] Hale, J.; Lunel, S.: Introduction to functional differential equations. (1993) · Zbl 0787.34002
[14] Hu, L.; Cao, Y.; Shao, H.: Constrained robust sampled-data control for nonlinear uncertain systems. International journal of robust and nonlinear control 12, 447-464 (2002) · Zbl 1026.93035
[15] Hu, L.; Lam, J.; Cao, Y.; Shao, H.: A LMI approach to robust H2 sampled-data control for linear uncertain systems. IEEE transaction systems man and cybernetics, B 33, 149-155 (2003)
[16] Kolmanovskii, V.; Myshkis, A.: Applied theory of functional differential equations. (1999) · Zbl 0917.34001
[17] Mikheev, Yu.V; Sobolev, V. A.; Fridman, E. M.: Asymptotic analysis of digital control systems. Automation and remote control 49, No. 9, 1175-1180 (1988) · Zbl 0692.93046
[18] Niculescu, S. I.; De Souza, C.; Dugard, L.; Dion, J. M.: Robust exponential stability of uncertain systems with time-varying delays. IEEE transactions on automatic control 43, No. 5, 743-748 (1998) · Zbl 0912.93053
[19] Oishi, Y.: A bound of conservativeness in sampled-data robust stabilization and its dependence on sampling periods. Systems and control letters 32, 11-19 (1997) · Zbl 0901.93039
[20] Osborn, S.; Bernstein, D.: An exact treatment of the achievable closed-loop H2-performance of sampled-data controllersfrom continuous-time to open-loop. Automatica 31, No. 4, 617-620 (1995)
[21] Sivashankar, N.; Khargonekar, P.: Characterization of the L2-induced norm for linear systems with jumps with applications to sampled-data systems. SIAM journal of control and optimization 32, 1128-1150 (1994) · Zbl 0802.93017
[22] Takaba, K.; Morihira, N.; Katayama, T.: A generalized Lyapunov theorem for descriptor systems. Systems and control letters 24, 49-51 (1995) · Zbl 0883.93035
[23] Tarbouriech, S.; Da Silva, J. Gomes: Synthesis of controllers for continuous-time delay systems with saturating controls via lmi’s. IEEE transactions on automatic control 45, No. 1, 105-111 (2000) · Zbl 0978.93062
[24] Trentelman, H.; Stoorvogel, A.: Sampled-data and discrete-time H2 optimal control. SIAM journal of control and optimization 33, No. 3, 834-862 (1995) · Zbl 0839.93050
[25] Yamamoto, Y. (1990). New approach to sampled-data control systems--a function space method. Proceedings of the 29th conference on decision and control, Honolulu, HW (pp. 1882-1887).