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Improved results on robust stability analysis and stabilization for a class of uncertain nonlinear systems. (English) Zbl 1206.93082
Summary: This paper deals with the problems of robust stability analysis and robust stabilization for uncertain nonlinear polynomial systems. The combination of a polynomial system stability criterion with an improved robustness measure of uncertain linear systems has allowed the formulation of a new criterion for robustness bound estimation of the studied uncertain polynomial systems. Indeed, the formulated approach is extended to involve the global stabilization of nonlinear polynomial systems with maximization of the stability robustness bound. The proposed method is helpful to improve the existing techniques used in the analysis and control for uncertain polynomial systems. Simulation examples illustrate the potential of the proposed approach.

93D09Robust stability of control systems
93D21Adaptive or robust stabilization
93C10Nonlinear control systems
Full Text: DOI EuDML
[1] S. Jannesari, “Stability analysis and stabilization of a class of nonlinear systems based on stability radii,” in International Conference on Control, Control, vol. 1, pp. 641-645, Swansea, UK, 1998. · doi:10.1049/cp:19980304
[2] J. Zhijian and W. Long, “Robust stability and stabilization of a class of nonlinearswitched systems,” in Proceedings of the 25th IASTED International Conference on Modelling, Indentification, and Control, pp. 37-42, Lanzarote, Spain, 2006.
[3] M. S. Mahmoud and N. B. Almutairi, “Robust stability and stabilization methods for a class of nonlinear discrete-time delay systems,” Applied Mathematics and Computation, vol. 215, no. 12, pp. 4280-4292, 2010. · Zbl 1194.93173 · doi:10.1016/j.amc.2009.12.054
[4] Y. Wang, L. Xie, and C. E. de Souza, “Robust control of a class of uncertain nonlinear systems,” Systems & Control Letters, vol. 19, no. 2, pp. 139-149, 1992. · Zbl 0765.93015
[5] D. F. Coutinho, M. Fu, and A. Trofino, “Robust analysis and control for a class of uncertain nonlinear discrete-time systems,” Systems & Control Letters, vol. 53, no. 5, pp. 377-393, 2004. · Zbl 1157.93465 · doi:10.1016/j.sysconle.2004.05.015
[6] J. Yoneyama, “Robust stability and stabilization for uncertain Takagi-Sugeno fuzzy time-delay systems,” Fuzzy Sets and Systems, vol. 158, no. 2, pp. 115-134, 2007. · Zbl 1110.93033 · doi:10.1016/j.fss.2006.09.004
[7] M. De la Sen, “Robust stability analysis and dynamic gain-scheduled controller design for point time-delay systems with parametrical uncertainties,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 6, pp. 1131-1156, 2008. · Zbl 1221.93209 · doi:10.1016/j.cnsns.2006.09.006
[8] V. F. Montagner, R. C. L. F. Oliveira, T. R. Calliero, R. A. Borges, P. L. D. Peres, and C. Prieur, “Robust absolute stability and nonlinear state feedback stabilization based on polynomial Lur’e functions,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 5, pp. 1803-1812, 2009. · Zbl 1155.93408 · doi:10.1016/j.na.2008.02.081
[9] R. V. Patel and M. Toda, “Quantitative measures of robustness for multivariable systems,” in Proceedings of Joint Automatic Control Conference, San Francisco, Calif, USA, 1980. · Zbl 0485.93068
[10] R. K. Yedavalli, “Flight control application of new stability robustness bound for linear uncertain systems,” Journal of Guidance, Control, and Dynamics, vol. 16, no. 6, pp. 1032-1037, 1993. · Zbl 0800.93992 · doi:10.2514/3.21124
[11] J. H. Kim, “Robust stability of linear systems with delayed perturbations,” IEEE Transactions on Automatic Control, vol. 41, no. 12, pp. 1820-1822, 1996. · Zbl 0944.93025 · doi:10.1109/9.545749
[12] J. D. Gardiner, “Computation of stability robustness bounds for state-space models with structured uncertainty,” IEEE Transactions on Automatic Control, vol. 42, no. 2, pp. 253-256, 1997. · Zbl 0866.93077 · doi:10.1109/9.554405
[13] X. Li and C. E. De Souza, “Criteria for robust stability and stabilization of uncertain linear systems with state delay,” Automatica, vol. 33, no. 9, pp. 1657-1662, 1997.
[14] F. Rotella and G. Dauphin-Tanguy, “Non-linear systems: identification and optimal control,” International Journal of Control, vol. 48, no. 2, pp. 535-544, 1988. · Zbl 0658.93026 · doi:10.1080/00207178808906195
[15] N. Benhadj Braiek, F. Rotella, and M. Benrejeb, “Algebraic criteria for global stability analysis of nonlinear systems,” International Journal of Systems Analysis Modelling and Simulation, vol. 17, pp. 221-227, 1995. · Zbl 0832.93050
[16] N. Benhadj Braiek, “On the global stability of nonlinear polynomial systems,” in Proceedings of the 35th IEEE Conference on Decision and Control (CDC ’96), Kobe, Japan, December 1996. · Zbl 0895.93036
[17] H. Bouzaouache and N. Benhadj Braiek, “On the stability analysis of nonlinear systems using polynomial Lyapunov functions,” Mathematics and Computers in Simulation, vol. 76, no. 5-6, pp. 316-329, 2008. · Zbl 1141.34033 · doi:10.1016/j.matcom.2007.04.001
[18] J. W. Brewer, “Kronecker products and matrix calculus in system theory,” IEEE Transactions on Circuits and Systems, vol. 25, no. 9, pp. 772-781, 1978. · Zbl 0397.93009 · doi:10.1109/TCS.1978.1084534
[19] R. Mtar, M. M. Belhaouane, H. Belkhiria Ayadi, and N. Benhadj Braiek, “An LMI criterion for the global stability analysis of nonlinear polynomial systems,” Nonlinear Dynamics and Systems Theory, vol. 9, no. 2, pp. 171-183, 2009. · Zbl 1183.34073 · http://www.sunrise-0014438.e-ndst.kiev.ua/v9n2/4(27).pdf
[20] M. M. Belhaouane, R. Mtar, H. Belkhiria Ayadi, and N. Benhadj Braiek, “An LMI technique for the global stabilization of nonlinear polynomial systems,” International Journal of Computers, Communications and Control, vol. 4, no. 4, pp. 335-348, 2009. · Zbl 1183.34073
[21] N. Benhadj Braiek and H. Belkhiria, “Robustness stability measure for a class of nonlinear uncertain systems,” in Proceedings of IEEE International Conference on Systems, Man, and Cybernetics (SMC ’99), vol. 1, pp. 28-32, Tokyo, Japan, October 1999.
[22] H. Belkhiria Ayadi and N. Benhadj Braiek, “Robust control of nonlinear polynomial systems,” in Proceedings of IEEE International Conference on Systems, Man, and Cybernetics (SMC ’99), vol. 4, pp. 1-5, Yasmine Hammamet, Tunisia, 2002. · Zbl 1291.78064 · doi:10.1109/ICSMC.2002.1173297
[23] N. Benhadj Braiek and F. Rotella, “Logid: a nonlinear systems identification software,” in Modelling and Simulation of Systems, pp. 211-218, Scientific Publishing, 1990.
[24] R. K. Yedavalli, “Improved measures of stability robustness for linear state space models,” IEEE Transactions on Automatic Control, vol. 30, no. 6, pp. 577-579, 1985. · Zbl 0557.93059 · doi:10.1109/TAC.1985.1103996
[25] R. K. Yedavalli and Z. Liang, “Reduced conservatism in stability robustness bounds by state transformation,” IEEE Transactions on Automatic Control, vol. 31, no. 9, pp. 863-866, 1986. · Zbl 0593.93040 · doi:10.1109/TAC.1986.1104408
[26] H. K. Khalil, Nonlinear Systems, Prentice-Hall, Upper Saddle River, NJ, USA, 3rd edition, 2000.
[27] T. Coleman, M. Ann Branch, and A. Grace, “Optimization toolbox for use withMatlab,” User’s guide, version 2, third printing revised for version 2 (Matlabrelease 11), January 1999.
[28] M. W. Spong, “Adaptive control of flexible joint manipulators,” Systems & Control Letters, vol. 13, no. 1, pp. 15-21, 1989. · Zbl 0691.93028
[29] F. Ghorbel, J. Y. Hung, and M. W. Spong, “Adaptative control of flexible joint manipulators,” in Proceedings of IEEE International Conference on Robotics and Automation, vol. 2, pp. 1188-1193, Scottsadale, Ariz, USA, May 1989.