Construction of strict Lyapunov function for nonlinear parameterised perturbed systems
الموضوعات :
1 - Faculty of science, University of Sfax, Sfax, Tunisia
2 - Faculty of science, University of Sfax, Sfax, Tunisia
الکلمات المفتاحية: Lyapunov function, Perturbed systems, uniform exponential stability,
ملخص المقالة :
In this paper, global uniform exponential stability of perturbed dynamical systemsis studied by using Lyapunov techniques. The system presents a perturbation term which isbounded by an integrable function with the assumption that the nominal system is globallyuniformly exponentially stable. Some examples in dimensional two are given to illustrate theapplicability of the main results.
[1] A. Benabdallah, M. Dlala and M. A. Hammami, A new Lyapunov function for stability of time-varying nonlinear perturbed systems. Systems and Control Letters, 56 (2007) 179-187.
[2] F. Camilli, L. Grne, F. Wirth, Zubovs method for perturbed differential equations, in: Proceedings of the Mathematical Theory of Networks and Systems, Perpignan, 2000, CD-ROM, article B100.
[3] F. Camilli, L. Grne, F. Wirth, A generalization of Zubovs method to perturbed systems. SIAM J. Control Optim. 40 (2001) 496-515.
[4] S. Dubljevic, N. Kazantzis, A new Lyapunov design approach for nonlinear systems based on Zubovs method. Automatica 38 (2002), 1999-2007.
[5] W. Hahn, Stability of Motion. Springer, Berlin, Heidelberg, 1967.
[6] M. A. Hammami, On the stability of nonlinear control systems with uncertainty. J. Dynamical Control Systems 7 (2) (2001), 171-179.
[7] H. K. Khalil, Nonlinear Systems. third ed., Prentice-Hall, Englewood Clifs, NJ, 2002.
[8] V. Lakshmikantham, S. Leela an A.A. Matynuk, Practical stability of nonlinear systems. World scientific Publishing Co. Pte. Ltd. 1990.
[9] Y. Lin, E. Sontag, Y. Wang, A smooth converse Lyapunov theorem for robust stability. SIAM J. Control Optim. 34 (1) (1996), 124-160.
[10] A. A. Martynuk, Stability in the models of real world phenomena. Nonlinear Dyn. Sys. Theory 11 (1) (2011), 7-52.
[11] F. Mazenc. Strict Lyapunov Fonctions for Time-varying Systems. Automatica 39 (2003), 349-353.
[12] D. R. Merkin, Introduction to the Theory of Stability. Springer, New York, Berlin, Heidelberg, 1996.
[13] E. Panteley, A. Loria, Global uniform asymptotic stability of cascaded nonautonomous nonlinear systems, in: Proceedings of the Fourth European Control Conference, Louvain-La-Neuve, Belgium, Julis, paper no. 259, 1996.
[14] E. Panteley, A. Loria, Growth rate conditions for uniform asymptotic stability of cascaded time-varying systems. Automatica 37 (2001) 453-460.
[15] V. N. Phat, Global stabilization for linear continuous time-varing systems. Applied Mathematics and Computation 175 (2006), 1730-1743.
[16] N. Rouche, P. Habets, M. Laloy, Stability theory by Lyapunovs direct method. Appl. Math. Sci. 22 (1977).
[17] R. Sepulchre, M. Jankovic, P.V. Kokotovic, Constructive Lyapunov stabilization of nonlinear cascade systems. IEEE Trans. Automat. Control 41 (12) (1996), 1723-1735.
