© The Institution of Engineering and Technology
The authors address control system design based on an interval observer for non-linear switched systems with non-linear vector functions that are assumed to satisfy Lipschitz conditions. First, the observer gain satisfying a Metzler matrix can be solved by optimisations of linear matrix inequalities (LMIs). Second, an interval observer is designed to estimate the states of non-linear switched systems with the average dwell time scheme, and sufficient conditions for state estimation are presented in terms of an LMI formulation. Third, based on an interval observer, state feedback matrices are designed to construct an asymptotically stabilising switching controller. Finally, a numerical example is provided to demonstrate the efficiency of the approach.
References
-
-
1)
-
20. Efimov, D., Ra”ıssi, T., Zolghadri, A.: ‘Control of nonlinear and LPV systems: interval observer-based framework’, IEEE Trans. Autom. Control, 2013, 58, (3), pp. 773–782 (doi: 10.1109/TAC.2013.2241476).
-
2)
-
16. Yu, L., Zheng, G., Boutat, D., et al : ‘Observability and observer design for a class of switched systems’, IET Control Theory Appl., 2011, 5, (9), pp. 1113–1119 (doi: 10.1049/iet-cta.2010.0475).
-
3)
-
24. Mazenc, F., Dinh, T.N., Niculescu, S.I.: ‘Robust interval observers and stabilization design for discrete-time systems with input and output’, Automatica, 2013, 49, pp. 3490–3497 (doi: 10.1016/j.automatica.2013.09.016).
-
4)
-
17. Yang, H., Jiang, B., Staroswiecki, M.: ‘Observer-based fault-tolerant control for a class of switched nonlinear systems’, IET Control Theory Appl., 2007, 1, (5), pp. 1523–1532 (doi: 10.1049/iet-cta:20060406).
-
5)
-
14. Xie, D., Chen, X.: ‘Observer-based switched control design for switched linear systems with time delay in detection of switching signal’, IET Control Theory Appl., 2008, 2, (5), pp. 437–445 (doi: 10.1049/iet-cta:20070212).
-
6)
-
18. Yuan, C., Wu, F.: ‘Hybrid control for switched linear systems with average dwell time’, IEEE Trans. Autom. Control, 2015, 60, pp. 240–245 (doi: 10.1109/TAC.2014.2322941).
-
7)
-
18. Ra”ıssi, T., Videau, G., Zolghadri, A.: ‘Interval observer design for consistency checks of nonlinear continuous-time systems’, Automatica, 2010, 46, pp. 518–527 (doi: 10.1016/j.automatica.2009.12.005).
-
8)
-
8. Mancilla-Aguilar, J.L.: ‘A condition for the stability of switched nonlinear systems’, IEEE Trans. Autom. Control, 2000, 45, (11), pp. 2077–2079 (doi: 10.1109/9.887629).
-
9)
-
9. Wang, Y., Gupta, V., Antsaklis, P.J.: ‘On passivity of a class of discrete-time switched nonlinear systems’, IEEE Trans. Autom. Control, 2014, 59, (3), pp. 692–702 (doi: 10.1109/TAC.2013.2287074).
-
10)
-
26. Smith, H.L.: ‘Monotone dynamical systems: An introduction to the theory of competitive and cooperative systems, volume 41 of surveys and monographs’ (AMS, Providence, RI, 1995).
-
11)
-
27. Nemirovski, G., Laub, A., Gahinet, A.J., et al : ‘LMI control toolbox for use with Matlab’ (The MathWorks Inc., 1995).
-
12)
-
16. Lu, B., Wu, F., Kim, S.: ‘Switching LPV control of an F-16 aircraft via controller state reset’, IEEE Trans. Control Syst. Technol., 2006, 14, (2), pp. 267–277 (doi: 10.1109/TCST.2005.863656).
-
13)
-
13. Caravani, P., Santis, E.D.: ‘Observer-based stabilization of linear switching systems’, Int. J. Robust Nonlinear Control, 2009, 19, pp. 1541–1563 (doi: 10.1002/rnc.1376).
-
14)
-
5. Zhai, G.S., Hu, B., Yasuda, K., Michel, A.N.: ‘Disturbance attenuation properties of time-controlled switched systems’, J. Franklin Inst., 2001, 338, (7), pp. 765–779 (doi: 10.1016/S0016-0032(01)00030-8).
-
15)
-
11. Zhao, J., Dimirovski, G.M.: ‘Quadratic stability of a class of switched nonlinear systems’, IEEE Trans. Autom. Control, 2004, 49, (4), pp. 574–578 (doi: 10.1109/TAC.2004.825611).
-
16)
-
22. Efimov, D., Ra”ıssi, T., Chebotarev, S., et al : ‘Interval state observer for nonlinear time varying systems’, Automatica, 2013, 49, (1), pp. 200–205 (doi: 10.1016/j.automatica.2012.07.004).
-
17)
-
23. Mazenc, F., Bernard, O.: ‘Interval observers for linear time-invariant systems with disturbances’, Automatica, 2011, 47, pp. 140–147 (doi: 10.1016/j.automatica.2010.10.019).
-
18)
-
1. Sun, Z., Ge, S.S.: ‘Switched linear systems: control and design’ (Springer-Verlag, 2005).
-
19)
-
21. Efimov, D., Perruquetti, W., Raïssi, T., et al : ‘Interval observers for time-varying discrete-time systems’, IEEE Trans. Autom. Control, 2013, 58, (12), pp. 3218–3224 (doi: 10.1109/TAC.2013.2263936).
-
20)
-
11. Branicky, M.S.: ‘Multiple Lyapunov functions and other analysis tools for switched and hybrid systems’, IEEE Trans. Autom. Control, 1998, 43, (4), pp. 475–482 (doi: 10.1109/9.664150).
-
21)
-
19. Ra”ıssi, T., Efimov, D., Zolghadri, A.: ‘Interval state estimation for a class of nonlinear systems’, IEEE Trans. Autom. Control, 2012, 57, (1), pp. 260–265 (doi: 10.1109/TAC.2011.2164820).
-
22)
-
25. Mazenc, F., Dinh, T.N.: ‘Construction of interval observers for continuous-time systems with discrete measurements’, Automatica, 2014, 50, (10), pp. 2555–2560 (doi: 10.1016/j.automatica.2014.08.008).
-
23)
-
15. Blanchini, F., Miani, S., Mesquine, F.: ‘A separation principle for linear switching systems and parametrization of all stabilizing controllers’, IEEE Trans. Autom. Control, 2009, 54, (2), pp. 279–292 (doi: 10.1109/TAC.2008.2010896).
-
24)
-
10. Chatterjee, D., Liberzon, D.: ‘On stability of randomly switched nonlinear systems’, IEEE Trans. Autom. Control, 2007, 52, (2), pp. 2390–2394 (doi: 10.1109/TAC.2007.904253).
-
25)
-
2. Liberzon, D.: ‘Switching in systems and control’ (Springer-Verlag, Berlin, 2003).
-
26)
-
21. Liberzon, D., Morse, A.S.: ‘Basic problems in stability and design of switched systems’, IEEE Control Syst. Mag., 1999, 19 (15), pp. 59–70 (doi: 10.1109/37.793443).
-
27)
-
2. Lin, H., Antsaklis, P.J.: ‘Stability and stabilization of switched linear systems: a survey of recent results’, IEEE Trans. Autom. Control, 2009, 54, (2), pp. 308–322 (doi: 10.1109/TAC.2008.2012009).
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2015.0285
Related content
content/journals/10.1049/iet-cta.2015.0285
pub_keyword,iet_inspecKeyword,pub_concept
6
6