© The Institution of Engineering and Technology
This study investigates the stabilisation of a class of continuoustime twodimensional (2D) switched nonlinear Roesser model with all modes unstable. Other than design controllers for the system, the authors would like to schedule the switching signal to achieve the asymptotical stability of the system. The main idea in this study is to utilise the alternative running of different subsystems to compensate the divergence of each subsystem, which thus achieves the stabilisation goal. By taking advantage of modedependent average dwell time property and a piecewise continuous Lyapunov function method, a general criterion is developed to guarantee the stability of the continuoustime switched 2D nonlinear system with a designed switching law. The obtained result is further used to deal with switched 2D linear system. Finally, the effectiveness and superiority of the proposed methods are illustrated by two numerical examples.
References


1)

1. Kaczorek, T.: ‘Twodimensional linear systems’ (Springer, Berlin, 1985).

2)

2. Wu, L., Wang, Z., Gao, H., et al: ‘Filtering for uncertain 2D discrete systems with state delays’, Signal Process., 2007, 87, (9), pp. 2213–2230.

3)

3. Li, X., Gao, H., Wang, C.: ‘Generalized KalmanYakubovichPopov lemma for 2D FMLSS model’, IEEE Trans. Autom. Control, 2012, 57, (12), pp. 3090–3103.

4)

4. Liang, J., Wang, Z., Liu, X.: ‘Robust state estimation for twodimensional stochastic timedelay systems with missing measurements and sensor saturation’, Multidimens. Syst. Signal Process., 2014, 25, (1), pp. 157–177.

5)

5. Fei, Z., Shi, S., Zhao, C., et al: ‘Asynchronous control for 2D switched systems with modedependent average dwell time’, Automatica, 2017, 79, pp. 198–206.

6)

6. Xu, S., Lam, J., Zou, Y., et al: ‘H∞ output feedback control for twodimensional continuous systems’, Dyn. Contin. Discrete Impulsive Syst. B, Appl. Algorithms, 2008, 1, (1), pp. 1–14.

7)

7. Lam, J., Xu, S., Zou, Y., et al: ‘Robust output feedback stabilization for twodimensional continuous systems in Roesser form’, Appl. Math. Lett., 2004, 17, (12), pp. 1331–1341.

8)

8. Emelianova, J.P., Pakshin, P.V., Galkowski, K., et al: ‘Stability of nonlinear 2D systems described by the continuoustime Roesser model’, Autom. Remote Control, 2014, 75, (5), pp. 845–858.

9)

9. Shi, S., Fei, Z., Sun, W., et al: ‘Stabilization of 2D switched systems with all modes unstable via switching signal regulation’, IEEE Trans. Autom. Control, 2017, .

10)

10. Ye, S., Wang, W.: ‘Stability analysis and stabilisation for a class of 2D nonlinear discrete systems’, Int. J. Syst. Sci., 2010, 42, (5), pp. 839–851.

11)

11. Ghous, I., Xiang, Z.: ‘Reliable H∞ control of 2D continuous nonlinear systems with time varying delays’, J. Franklin Inst., 2015, 352, (12), pp. 5758–5778.

12)

12. Dai, J., Guo, G.: ‘Delaydependent stability and H∞ control for 2D Markovian jump delay systems with missing measurements and sensor nonlinearities’, Circuits Syst. Signal Process., 2017, 36, (1), pp. 25–48.

13)

13. MancillaAguilar, J.L., Garcĺła, R.A.: ‘Robustness properties of an algorithm for the stabilisation of switched systems with unbounded perturbations’, Int. J. Control, 2017, 90, (5), pp. 961–973.

14)

14. Ahn, C.K., Wu, L., Shi, P.: ‘Stochastic stability analysis for 2D Roesser systems with multiplicative noise’, Automatica, 2016, 69, pp. 356–363.

15)

15. Chen, S.F., Fong, I.K.: ‘Delaydependent robust H∞ filtering for uncertain 2D statedelayed systems’, Signal Process., 2007, 87, (11), pp. 2659–2672.

16)

16. Wu, Z., Cui, M., Shi, P., et al: ‘Stability of stochastic nonlinear systems with statedependent switching’, IEEE Trans. Autom. Control, 2013, 58, (8), pp. 1904–1918.

17)

17. Li, Z., Yu, Z., Zhao, H.: ‘Further result on H∞ filter design for continuoustime Markovian jump systems with timevarying delay’, J. Franklin Inst., 2014, 351, (9), pp. 4619–4635.

18)

18. Zhang, L., Shi, P.: ‘Stability, l2gain and asynchronous H∞ control of discretetime switched systems with average dwell time’, IEEE Trans. Autom. Control, 2009, 54, (9), pp. 2192–2199.

19)

19. Zhang, L., Zhuang, S., Shi, P.: ‘Nonweighted quasitimedependent H∞, filtering for switched linear systems with persistent dwelltime’, Automatica, 2015, 54, pp. 201–209.

20)

20. Liu, J., Vazquez, S., Wu, L., et al: ‘Extended state observerbased slidingmode control for threephase power converters’, IEEE Trans. Ind. Electron., 2017, 64, (1), pp. 22–31.

21)

21. Fei, Z., Shi, S., Wang, Z., et al: ‘Quasitimedependent output control for discretetime switched system with mode dependent average dwell time’, IEEE Trans. Autom. Control, 2017, doi: 10.1109/TAC.2017.2771373.

22)

22. Benzaouia, A., Hmamed, A., Tadeo, F.: ‘Stability conditions for discrete 2D switching systems, based on a multiple Lyapunov function’. European Control Conf., Budapest, Hungary, 2009, pp. 23–26.

23)

23. Benzaouia, A., Hmamed, A., Tadeo, F., et al: ‘Stabilisation of discrete 2D time switching systems by state feedback control’, Int. J. Syst. Sci., 2011, 42, (3), pp. 479–487.

24)

24. Duan, Z., Xiang, Z., Karimi, H.R.: ‘Delaydependent H∞ control for discrete 2D switched delay systems in the second FM model’, J. Franklin Inst., 2013, 350, (7), pp. 1697–1718.

25)

25. Wu, L., Yang, R., Shi, P., et al: ‘Stability analysis and stabilization of 2D switched systems under arbitrary and restricted switchings’, Automatica, 2015, 59, pp. 206–215.

26)

26. Huang, S., Xiang, Z.: ‘Stability analysis of twodimensional switched nonlinear continuoustime systems’, IET Control Theory Appl., 2016, 10, (6), pp. 724–729.

27)

27. Zhao, X., Zhang, L., Shi, P., et al: ‘Stability and stabilization of switched linear systems with modedependent average dwell time’, IEEE Trans. Autom. Control, 2012, 57, (7), pp. 1809–1815.

28)

28. Zhao, X., Shi, P., Yin, Y., et al: ‘New results on stability of slowly switched systems: a multiple discontinuous Lyapunov function approach’, IEEE Trans. Autom. Control, 2017, 62, (7), pp. 3502–3509.

29)

29. Allerhand, L.I., Shaked, U.: ‘Robust stability and stabilization of linear switched systems with dwell time’, IEEE Trans. Autom. Control, 2011, 56, (2), pp. 381–386.

30)

30. Xiang, W., Xiao, J.: ‘Stabilization of switched continuoustime systems with all modes unstable via dwell time switching’, Automatica, 2014, 50, pp. 940–945.

31)

31. Hmamed, A., Kririm, S., Benzaouia, A., et al: ‘Delaydependent stability and stabilisation of continuous 2D delayed systems with saturating control’, Int. J. Syst. Sci., 2016, 47, (12), pp. 3004–3015.
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