Title:
|
Bounded-input-bounded-state stabilization of switched processes and periodic asymptotic controllability (English) |
Author:
|
Bacciotti, Andrea |
Language:
|
English |
Journal:
|
Kybernetika |
ISSN:
|
0023-5954 (print) |
ISSN:
|
1805-949X (online) |
Volume:
|
53 |
Issue:
|
3 |
Year:
|
2017 |
Pages:
|
530-544 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
The main result of this paper is a sufficient condition for the existence of periodic switching signals which render asymptotically stable at the origin a linear switched process defined by a pair of $2\times 2$ real matrices. The interest of this result is motivated by the application to the problem of bounded-input-bounded-state (with respect to an external input) stabilization of linear switched processes. (English) |
Keyword:
|
switched processes |
Keyword:
|
asymptotic controllability |
Keyword:
|
bounded-input-bounded-state stability |
MSC:
|
93B60 |
MSC:
|
93D20 |
idZBL:
|
Zbl 06819622 |
idMR:
|
MR3684684 |
DOI:
|
10.14736/kyb-2017-3-0530 |
. |
Date available:
|
2017-11-12T09:48:41Z |
Last updated:
|
2018-01-10 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146941 |
. |
Reference:
|
[1] Bacciotti, A.: Periodic open-loop stabilization of planar switched systems..Europ. J. Control 21 (2015), 22-27. MR 3426567, 10.1016/j.ejcon.2015.09.002 |
Reference:
|
[2] Bacciotti, A.: Periodic asymptotic controllability of switched systems..Libertas Mathematica (new series) 34 (2014), 23-46. MR 3337805, 10.14510/lm-ns.v34i1.1287 |
Reference:
|
[3] Bacciotti, A., Mazzi, L.: Asymptotic controllability by means of eventually periodic switching rules..SIAM J. Control Optim. 49 (2011), 476-497. MR 2784697, 10.1137/100798260 |
Reference:
|
[4] Brockett, R. W.: Finite Dimensional Linear Systems..Wiley, New York 1970. MR 3486166, 10.1137/1.9781611973884 |
Reference:
|
[5] Ceragioli, F.: Finite valued feedback laws and piecewise classical solutions..Nonlinear Analysis 65 (2006), 984-998. MR 2232489, 10.1016/j.na.2005.10.030 |
Reference:
|
[6] Conti, R.: Asymptotic control..In: Control Theory and Topics in Functional Analysis, International Atomic Energy Agency, Vienna 1976, pp. 329-360. MR 0529108 |
Reference:
|
[7] Conti, R.: Linear Differential Equations and Control..Academic Press, London 1976. MR 0513642 |
Reference:
|
[8] Lin, H., Antsaklis, P. J.: Stability and stabilization of switched linear systems: a survey of recent results..IEEE Trans. Automat. Control 54 (2009), 308-322. MR 2491959, 10.1109/tac.2008.2012009 |
Reference:
|
[9] Huang, Z., Xiang, C., Lin, H., Lee, T.: Necessary and sufficient conditions for regional stabilisability of generic switched linear systems with a pair of planar subsystems..Int. J. Control 83 (2010), 694-715. MR 2666164, 10.1080/00207170903384321 |
Reference:
|
[10] Kundu, A., Chatterjee, D., Liberzon, D.: Generalized switching signals for input-to-state stability of switched systems..Automatica 64 (2016), 270-277. MR 3433105, 10.1016/j.automatica.2015.11.027 |
Reference:
|
[11] Liberzon, D.: Switching in Systems and Control..Birkhäuser, Boston 2003. Zbl 1036.93001, MR 1987806, 10.1007/978-1-4612-0017-8 |
Reference:
|
[12] Sontag, E. D.: Mathematical Control Theory..Springer-Verlag, New York 1990. Zbl 0945.93001, MR 1070569, 10.1007/978-1-4684-0374-9 |
Reference:
|
[13] Sontag, E. D.: Smooth stabilization implies coprime factorization..IEEE Trans. Automat. Control 34 (1989), 435-443. MR 0987806, 10.1109/9.28018 |
Reference:
|
[14] Sun, Z., Ge, S. S.: Switched Linear Systems..Springer-Verlag, London 2005. 10.1007/1-84628-131-8 |
Reference:
|
[15] Tokarzewski, J.: Stability of periodically switched linear systems and the switching frequency..Int. J. Systems Sci. 18 (1987), 698-726. MR 0880945, 10.1080/00207728708964001 |
Reference:
|
[16] Vu, L., Chatterjee, D., Liberzon, D.: Input-to-state stability of switched systems and switching adaptive control..Automatica 43 (2007), 639-646. MR 2306707, 10.1016/j.automatica.2006.10.007 |
Reference:
|
[17] Feng, Wei, Zhang, JiFeng: Input-to-state stability of switched nonlinear systems..Science in China Series F: Information Sciences 51 (2008), 1992-2004. MR 2460755, 10.1007/s11432-008-0161-7 |
Reference:
|
[18] Wicks, M., Peleties, P., DeCarlo, R. A.: Switched controller synthesis for the quadratic stabilization of a pair of unstable linear systems..Europ. J. Control 4 (1998), 140-147. 10.1016/s0947-3580(98)70108-6 |
Reference:
|
[19] Willems, J. L.: Stability Theory of Dynamical Systems..Nelson, London 1970. |
Reference:
|
[20] Xu, X., Antsaklis, P. J.: Stabilization of second-order LTI switched systems..Int. J. Control 73 (2000), 1261-1279. MR 1783084, 10.1080/002071700421664 |
Reference:
|
[21] Yang, G., Liberzon, D.: Input-to-state stability for switched systems with unstable subsystems: A hybrid Lyapunov construction..In: Proc. IEEE Conference on Decision and Control 2014 (2015), pp. 6240-6245. 10.1109/cdc.2014.7040367 |
Reference:
|
[22] Yoshizawa, T.: Stability Theory by Liapunov's Second Method..Publications of the Mathematical Society of Japan No. 9, 1966. MR 0208086 |
Reference:
|
[23] Wang, Yue-E, Sun, Xi-Ming, Shi, Peng, Zhao, Jun: Input-to-State stability of switched nonlinear systems with time delays under asynchronous switching..IEEE Trans. Cybernetics 43 (2013), 2261-2265. 10.1109/tcyb.2013.2240679 |
Reference:
|
[24] Wang, Yue-E, Sun, Xi-Ming, Wang, Wei, Zhao, Jun: Stability properties of switched nonlinear delay systems with synchronous or asynchronous switching..Asian J. Control 17 (2015), 1187-1195. MR 3373079, 10.1002/asjc.964 |
. |