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Journal of Applied Nonlinear Dynamics 10(4) (2021) 659--669 | DOI:10.5890/JAND.2021.12.006

H. Damak

University of Sfax, Faculty of Sciences of Sfax, Department of Mathematics, Road of Soukra BP1171, 3000 Sfax, Tunisia

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Abstract

This paper investigates the problem of output feedback $h$-stabilization of nonlinear uncertain systems. We construct an output feedback controller that guarantees global uniform practical $h$-stability of the closed-loop system. Our original results generalize well-known fundamental results: practical stability, practical asymptotic stability and practical exponential stability for nonlinear time-varying systems. Finally, two numerical examples are presented to demonstrate the validity of the proposed method.

References

1. [1]	Barmish, B.R. and Leitmann, G. (1982), On ultimate boundedness control of uncertain systems in the absence of matching assumptions, IEEE T. Automat. Control, 27, 153-158.

2. [2]	Benabdallah, A. (2009), On the practical output feedback stabilization for nonlinear uncertain systems, Nonlinear Anal. Model., 14, 145-153.

3. [3]	Benabdallah, A. and Hammami, M.A. (2001), On the output feedback stability for non-linear uncertain control systems, Int. J. Control., 74, 547-551.

4. [4]	Corless, M. (1990), Guaranteed rates of exponential convergence for uncertain systems, J. Optim. Theory Appl., 64, 481-494.

5. [5]	Corless, M. and Leitmann, G. (1981), Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems, IEEE T. Automat. Control, 26, 1139-1143.

6. [6]	Corless, M. and Leitmann, G. (1993), Bounded controllers for robust exponential convergence, J. Optim. Theory Appl., 76, 1-12.

7. [7]	Khalil, H.K. (2002), Nonlinear systems, Prentice-Hall, New York.

8. [8]	Soldatos, A.G. and Corless, M. (1991), stabilizing uncertain systems with bounded control, Dynam. Control, 1 , 227-238.

9. [9]	Wu, H. and Mizukami, K. (1993), Exponential stability of a class of nonlinear dynamical systems with uncertainties, Systems Control Letters, 21, 307-313.

10. [10]	Steinberg, A. and Corless M. (1985), Output feedback stabilization of uncertain dynamical systems, IEEE Trans. Automat. Contr., 30, 1025-1027.

11. [11]	Walcott, B. (1988), Nonlinear output stabilization ot uncertain systems, Proe. American Control Conference, 2253-2258.

12. [12]	Phat, V.N. (2006), Global stabilization for linear continuous time-varying systems, Appl. Math. Comput., 175, 1730-1743.

13. [13]	Chen, H., Zhang, J., Chen, B. and Haitao, C. (2013), Robust synchronization of incommensurate fractional-order chaotic systems via second-order sliding mode technique, J. Appl. Math., http://dx.doi.org/10.1155/2013/321253.

14. [14]	Chen, H., Zhang, J., Chen, B., and Baoujun, L. (2013), Global practical stabilization for non-holonomic mobile robots with uncalibrated visual parameters by using a switching controller, IMA J. Math. Control Info. 30, 543-557.

15. [15]	Damak, H., Hammami, M.A., and Kalitine, B. (2014), On the global uniform asymptotic stability of time-varying systems, Diff. Equ. Dyn. Syst., 22, 113-124.

16. [16]	Benabdallah, A. and Hammami, M.A. (2008), Bounded controller for uncertain nonlinear systems, J. Appl. Analysis, 14, 239-249.

17. [17]	Ghanmi, B. (2019), On the practical $h$-stability of nonlinear systems of differential equations, J. Dyn. Control Syst., 25, 1-23.

18. [18]	Pinto, M. (1984), Perturbations of asymptotically stable differential equations, Analysis,4, 161-175.

19. [19]	Pinto, M. (1992), Stability of nonlinear differential system, Applicable Analysis 43, 1-20.

20. [20]	Pinto, M. (1988), Asymptotic integration of a system resulting from the perturbation of an $h$-system, J. Math. Anal. Appl., 131, 194-216.

21. [21]	Zhoo, B. (2017), Stability analysis of nonlinear time-varying systems by Lyapunov functions with indefinite derivatives, IET Control Theory Appl., 11, 1434-1442.