Stability and control synthesis for discrete-time linear systems subject to actuator saturation by output feedback

Benzaouia, A.; Mesquine, F.; Hmamed, A.; Aoufoussi, H.

doi:https://doi.org/10.1155/MPE/2006/43970

Mathematical Problems in Engineering

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Volume 2006 | Article ID 043970 | https://doi.org/10.1155/MPE/2006/43970

Stability and control synthesis for discrete-time linear systems subject to actuator saturation by output feedback

A. Benzaouia,¹F. Mesquine,¹A. Hmamed,²and H. Aoufoussi³

Received16 Aug 2004

Revised15 Sept 2005

Accepted22 Sept 2005

Published19 Mar 2006

Abstract

This paper presents sufficient conditions of asymptotic stability for discrete-time linear systems subject to actuator saturations with an output feedback law. The derived stability results are given in terms of LMIs. A new proof is presented to obtain previous conditions of asymptotic stability. A numerical example is used to illustrate this technique by using a linear optimization problem subject to LMI constraints.

References

A. Benzaouia and A. Baddou, “Piecewise linear constrained control for continuous-time systems,” IEEE Transactions on Automatic Control, vol. 44, no. 7, pp. 1477–1481, 1999.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
A. Benzaouia, A. Baddou, and S. Elfaiz, “Piecewise linear constrained control for continuous-time systems: the maximal admissible domain,” in Proceedings of 15th IFAC World Congress, Barcelona, 2002.
View at: Google Scholar
A. Benzaouia, E. L. Boukas, and N. Daraoui, “Stability of continuous-time linear systems with Markovian jumping parameters and constrained control,” in Proceedings of 15th IFAC World Congress, Barcelona, 2002.
View at: Google Scholar
A. Benzaouia and C. Burgat, “Regulator problem for linear discrete-time systems with non-symmetrical constrained control,” International Journal of Control, vol. 48, no. 6, pp. 2441–2451, 1988.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
A. Benzaouia and A. Hmamed, “Regulator problem for linear continuous-time systems with nonsymmetrical constrained control,” IEEE Transactions on Automatic Control, vol. 38, no. 10, pp. 1556–1560, 1993.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
A. Benzaouia and D. Mehdi, “The output feedback saturated controller design for linear systems,” in Proceedings of the 10th Mediterranean Conferenceon Control and Automation, Lisbon, 2002.
View at: Google Scholar
D. S. Bernstein and A. N. Michel, “A chronological bibliography on saturating actuators,” International Journal of Robust and Nonlinear Control, vol. 5, no. 5, pp. 375–380, 1995.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
F. Blanchini, “Set invariance in control,” Automatica, vol. 35, no. 11, pp. 1747–1767, 1999.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
E. K. Boukas and A. Benzaouia, “Stability of discrete-time linear systems with Markovian jumping parameters and constrained control,” IEEE Transactions on Automatic Control, vol. 47, no. 3, pp. 516–521, 2002.
View at: Publisher Site | Google Scholar | MathSciNet
Y.-Y. Cao and Z. Lin, “Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function,” in Proceedings of 41st IEEE Conference on Decision and Control, vol. 4, pp. 4140–4145, Nevada, 2002.
View at: Google Scholar
E. B. Castelan and S. Tarbouriech, “On positive invariance and output feedback stabilization of input constrained linear systems,” in Proceedings of American Control Conference, vol. 3, pp. 2740–2745, Maryland, 1994.
View at: Google Scholar
J. Daafouz, P. Riedinger, and C. Iung, “Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach,” IEEE Transactions on Automatic Control, vol. 47, no. 11, pp. 1883–1887, 2002.
View at: Publisher Site | Google Scholar | MathSciNet
L. El Ghaoui, F. Oustry, and M. AitRami, “A cone complementarity linearization algorithm for static output-feedback and related problems,” IEEE Transactions on Automatic Control, vol. 42, no. 8, pp. 1171–1176, 1997.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
H. Fang, Z. Lin, and T. Hu, “Analysis of linear systems in the presence of actuator saturation and $\mathcal {L}_2$ -disturbances,” Automatica, vol. 40, no. 7, pp. 1229–1238, 2004.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
G. Garcia, B. Pradin, and F. Zeng, “Stabilization of discrete time linear systems by static output feedback,” IEEE Transactions on Automatic Control, vol. 46, no. 12, pp. 1954–1958, 2001.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
E. G. Gilbert and K. T. Tan, “Linear systems with state and control constraints: the theory and application of maximal output admissible sets,” IEEE Transactions on Automatic Control, vol. 36, no. 9, pp. 1008–1020, 1991.
View at: Publisher Site | Google Scholar | MathSciNet
C. Gökçek, P. T. Kabamba, and S. M. Meerkov, “An LQR/LQG theory for systems with saturating actuators,” IEEE Transactions on Automatic Control, vol. 46, no. 10, pp. 1529–1542, 2001.
View at: Google Scholar | MathSciNet
D. Henrion, S. Tarbouriech, and G. Garcia, “Output feedback robust stabilization of uncertain linear systems with saturating controls: an LMI approach,” IEEE Transactions on Automatic Control, vol. 44, no. 11, pp. 2230–2237, 1999.
View at: Publisher Site | Google Scholar | MathSciNet
H. Hindi and S. Boyd, “Analysis of linear systems with saturating using convex optimization,” in Proceeding of the 37th IEEE Conference on Decision and Control, vol. 1, pp. 903–908, Florida, 1998.
View at: Google Scholar
T. Hu and Z. Lin, “The equivalence of several set invariance conditions under saturation,” in Procceding of the 41st IEEE Conference on Decision and Control, vol. 4, pp. 4146–4147, Nevada, 2002.
View at: Google Scholar
T. Hu, Z. Lin, and B. M. Chen, “An analysis and design method for linear systems subject to actuator saturation and disturbance,” Automatica, vol. 38, no. 2, pp. 351–359, 2002.
View at: Publisher Site | Google Scholar
T. Hu, Z. Lin, and B. M. Chen, “Analysis and design for discrete-time linear systems subject to actuator saturation,” Systems & Control Letters, vol. 45, no. 2, pp. 97–112, 2002.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
H. Kimura, “Pole assignment by gain output feedback,” IEEE Transactions on Automatic Control, vol. 20, no. 4, pp. 509–516, 1975.
View at: Publisher Site | Google Scholar | MathSciNet
F. Mesquine and A. Benzaouia, “Existence of output feedback for the regulator problem of a class of systems with constrained control,” in Proceedeings of the 1st International Conference on Electronics and Automatic, vol. 4, pp. 108–116, Tizi Ouzou, 1992.
View at: Google Scholar
F. Mesquine, F. Tadeo, and A. Benzaouia, “Regulator problem for linear systems with constraints on control and its increment or rate,” Automatica, vol. 40, no. 8, pp. 1387–1395, 2004.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
E. D. Sontag and H. J. Sussmann, “Nonlinear output feedback design for linear systems with saturating controls,” in Proceedings of the 29th IEEE Conference on Decision and Control, vol. 6, pp. 3414–3416, Hawaii, 1990.
View at: Google Scholar
V. L. Syrmos, C. Abdallah, and P. Dorato, “Static output feedback: a survey,” in Proceedings of the 33rd IEEE Conference on Decision and Control, vol. 1, pp. 837–842, Florida, 1994.
View at: Google Scholar

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Copyright © 2006 A. Benzaouia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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