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Keywords:
switched processes; asymptotic controllability; bounded-input-bounded-state stability
switched processes; asymptotic controllability; bounded-input-bounded-state stability
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.
References:
[1] Bacciotti, A.: Periodic open-loop stabilization of planar switched systems. Europ. J. Control 21 (2015), 22-27. DOI 10.1016/j.ejcon.2015.09.002 | MR 3426567
[2] Bacciotti, A.: Periodic asymptotic controllability of switched systems. Libertas Mathematica (new series) 34 (2014), 23-46. DOI 10.14510/lm-ns.v34i1.1287 | MR 3337805
[3] Bacciotti, A., Mazzi, L.: Asymptotic controllability by means of eventually periodic switching rules. SIAM J. Control Optim. 49 (2011), 476-497. DOI 10.1137/100798260 | MR 2784697
[4] Brockett, R. W.: Finite Dimensional Linear Systems. Wiley, New York 1970. DOI 10.1137/1.9781611973884 | MR 3486166
[5] Ceragioli, F.: Finite valued feedback laws and piecewise classical solutions. Nonlinear Analysis 65 (2006), 984-998. DOI 10.1016/j.na.2005.10.030 | MR 2232489
[6] Conti, R.: Asymptotic control. In: Control Theory and Topics in Functional Analysis, International Atomic Energy Agency, Vienna 1976, pp. 329-360. MR 0529108
[7] Conti, R.: Linear Differential Equations and Control. Academic Press, London 1976. MR 0513642
[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. DOI 10.1109/tac.2008.2012009 | MR 2491959
[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. DOI 10.1080/00207170903384321 | MR 2666164
[10] Kundu, A., Chatterjee, D., Liberzon, D.: Generalized switching signals for input-to-state stability of switched systems. Automatica 64 (2016), 270-277. DOI 10.1016/j.automatica.2015.11.027 | MR 3433105
[11] Liberzon, D.: Switching in Systems and Control. Birkhäuser, Boston 2003. DOI 10.1007/978-1-4612-0017-8 | MR 1987806 | Zbl 1036.93001
[12] Sontag, E. D.: Mathematical Control Theory. Springer-Verlag, New York 1990. DOI 10.1007/978-1-4684-0374-9 | MR 1070569 | Zbl 0945.93001
[13] Sontag, E. D.: Smooth stabilization implies coprime factorization. IEEE Trans. Automat. Control 34 (1989), 435-443. DOI 10.1109/9.28018 | MR 0987806
[14] Sun, Z., Ge, S. S.: Switched Linear Systems. Springer-Verlag, London 2005. DOI 10.1007/1-84628-131-8
[15] Tokarzewski, J.: Stability of periodically switched linear systems and the switching frequency. Int. J. Systems Sci. 18 (1987), 698-726. DOI 10.1080/00207728708964001 | MR 0880945
[16] Vu, L., Chatterjee, D., Liberzon, D.: Input-to-state stability of switched systems and switching adaptive control. Automatica 43 (2007), 639-646. DOI 10.1016/j.automatica.2006.10.007 | MR 2306707
[17] Feng, Wei, Zhang, JiFeng: Input-to-state stability of switched nonlinear systems. Science in China Series F: Information Sciences 51 (2008), 1992-2004. DOI 10.1007/s11432-008-0161-7 | MR 2460755
[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. DOI 10.1016/s0947-3580(98)70108-6
[19] Willems, J. L.: Stability Theory of Dynamical Systems. Nelson, London 1970.
[20] Xu, X., Antsaklis, P. J.: Stabilization of second-order LTI switched systems. Int. J. Control 73 (2000), 1261-1279. DOI 10.1080/002071700421664 | MR 1783084
[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. DOI 10.1109/cdc.2014.7040367
[22] Yoshizawa, T.: Stability Theory by Liapunov's Second Method. Publications of the Mathematical Society of Japan No. 9, 1966. MR 0208086
[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. DOI 10.1109/tcyb.2013.2240679
[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. DOI 10.1002/asjc.964 | MR 3373079
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