© The Institution of Engineering and Technology
In this study, the stabilisation of quasi-one-sided Lipschitz non-linear systems is investigated. For the quasi-one-sided Lipschitz non-linear system, a condition for the existence of the observer is presented. For the weak quasi-one-sided Lipschitz non-linear system, a state feedback controller is proposed and a condition is derived for the existence of the state feedback controller. The separation principle is obtained for the observer-based controller of the quasi-one-sided Lipschitz non-linear systems. The main results in this study extend and improve those in the literature. Numerical examples are given to illustrate the main results.
References
-
-
1)
-
7. Raghavan, S., Hedrick, J.K.: ‘Observer design for a class of nonlinear systems’, Int. J. Control, 1994, 59, pp. 515–528.
-
2)
-
11. Hu, G.D.: ‘Observers for one-sided Lipschitz non-linear systems’, IMA J. Math. Control Inf., 2006, 23, pp. 395–401.
-
3)
-
17. Barbata, A., Zasadzinski, M., Ali, H., et al: ‘Exponential observer for a class of one-sided Lipschitz stochastic nonlinear systems’, IEEE Trans. Autom. Control, 2015, 60, pp. 259–264.
-
4)
-
21. Nguyen, C.M., Pathirana, P.N., Trinh, H.: ‘Robust observer and observer-based control designs for discrete one-sided Lipschitz systems subject to uncertainties and disturbances’, Appl. Math. Comput., 2019, 353, pp. 42–53.
-
5)
-
2. Fossen, T.I., Strand, J.P.: ‘Passive nonlinear observer design for ships using Lyapunov methods: full-scale experiments with a supply vessel’, Automatica, 1999, 35, pp. 3–16.
-
6)
-
15. Badreddine, E.H., Hicham, E.A., Abdelaziz, H., et al: ‘New approach to robust observer-based control of one-sided Lipschitz non-linear systems’, IET Control Theory Applic., 2019, 13, pp. 333–342.
-
7)
-
5. Fu, F., Hou, M., Duan, G.: ‘Stabilization of quasi-one-sided Lipschitz nonlinear systems’, IMA J. Math. Control. Inf., 2013, 30, pp. 169–184.
-
8)
-
1. Aguilar, L., Orlov, Y., Acho, L.: ‘Nonlinear H∞-control of nonsmooth time-varying systems with application to friction mechanical manipulators’, Automatica, 2003, 39, pp. 1531–1542.
-
9)
-
18. Beikzadeh, H., Marquez, H.J.: ‘Input-to-error stable observer for nonlinear sampled-data systems with application to one-sided Lipschitz systems’, Automatica, 2016, 67, pp. 1–7.
-
10)
-
20. Nguyen, C.M., Pathirana, P.N., Trinh, H.: ‘Robust observer-based control designs for discrete nonlinear systems with disturbances’, Eur. J. Control, 2018, 44, pp. 65–72.
-
11)
-
12. Hu, G.D.: ‘A note on observers for one-sided Lipschitz non-linear systems’, IMA J. Math. Control Inf., 2008, 25, pp. 297–303.
-
12)
-
23. Peterson, I.R., Hollot, C.V.: ‘A Ricatti equation approach to the stabilization of uncertain linear systems’, Automatica, 1986, 22, pp. 397–411.
-
13)
-
4. Khalil, H.K.: ‘Nonlinear control’ (Pearson Education Limited, Boston, 2015).
-
14)
-
13. Xu, M., Hu, G.D., Zhao, Y.: ‘Reduced-order observer design for one-sided Lipschitz non-linear systems’, IMA J. Math. Control Inf., 2009, 26, pp. 299–317.
-
15)
-
10. Dekker, K., Verwer, J.G.: ‘Stability of Runge–Kutta methods for stiff nonlinear differential equations’ (North-Holland, Amsterdam, 1984).
-
16)
-
8. Rajamani, R.: ‘Observer for Lipschitz nonlinear systems’, IEEE Trans. Autom. Control, 1998, 43, pp. 397–401.
-
17)
-
22. Nguyen, C.M., Pathirana, P.N., Trinh, H.: ‘Reduced-order observer design for one-sided Lipschitz time-delay systems subject to unknown inputs’, IET Control Theory Applic., 2016, 10, pp. 1097–1105.
-
18)
-
19. Benallouch, M., Boutayeb, M., Zasadzinski, M.: ‘Observer design for one-sided Lipschitz discrete-time systems’, Syst. Control Lett., 2012, 61, pp. 879–886.
-
19)
-
14. Zhao, Y., Tao, J., Shi, N.Z.: ‘A note on observer design for one-sided Lipschitz nonlinear systems’, Syst. Control Lett., 2010, 59, pp. 66–71.
-
20)
-
9. Thau, F.E.: ‘Observing the sate of nonlinear dynamic systems’, Int. J. Control, 1973, 17, (3), pp. 471–480.
-
21)
-
6. Krener, A.J., Isidori, A.: ‘Linearization by output injection and nonlinear observers’, Syst. Control Lett., 1983, 3, pp. 47–52.
-
22)
-
3. Karafyllis, I., Kravaris, C.: ‘Robust output feedback stabilization and nonlinear observer design’, Syst. Control Lett., 2005, 54, pp. 925–938.
-
23)
-
16. Saad, W., Sellami, A., Garcia, G.: ‘Robust integral sliding mode-H∞ control of one-sided Lipschitz non-linear systems’, IET Control Theory Applic., 2018, 12, pp. 2357–2367.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2019.0230
Related content
content/journals/10.1049/iet-cta.2019.0230
pub_keyword,iet_inspecKeyword,pub_concept
6
6