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Stabilization of switched linear systems with time-delay in detection of switching signal. (English) Zbl 1140.93463

Summary: A feedback stabilization problem for switched linear systems with time-delay in detection of switching signal is formulated. First, online state feedback controller design method for asymptotic stability and exponential stability is given. Then, offline state feedback controller design method for asymptotic stability and exponential stability is given as well.

MSC:

93D15 Stabilization of systems by feedback
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[1] Ezzine, J.; Haddad, A. H., Controllability and observability of hybrid systems, Internat. J. Control, 49, 2045-2055 (1989) · Zbl 0683.93011
[2] Sun, Z.; Zheng, D. Z., On reachability and stabilization of switched linear systems, IEEE Trans. Automat. Control, 46, 291-295 (2001) · Zbl 0992.93006
[3] Xie, G.; Zheng, D. Z., On the controllability and reachability of a class of hybrid dynamical systems, (Proc. 19th Chinese Control Conference, vol. 1 (2000)), 114-117
[4] Xie, G.; Wang, L., Necessary and sufficient conditions for controllability of switched linear systems, (Proc. American Control Conference (2002)), 1897-1902 · Zbl 0531.93011
[5] Xie, G.; Wang, L., Controllability and stabilizability of switched linear systems, Systems Control Lett., 48, 135-155 (2003) · Zbl 1134.93403
[6] Xie, G.; Wang, L.; Wang, Y., Controllability of periodically switched linear systems with delay in control, (Proc. 15th Int. Symp. Mathematical Theory of Networks and Systems (2002), University of Notre Dame)
[7] Liberzon, D.; Morse, A. S., Basic problems in stability and design of switched systems, IEEE Contr. Syst. Mag., 19, 59-70 (1999) · Zbl 1384.93064
[8] Liberzon, D.; Hespanha, J. P.; Morse, A. S., Stability of switched systems: a Lie-algebraic condition, Systems Control Lett., 37, 117-122 (1999) · Zbl 0948.93048
[9] Narendra, K. S.; Balakrishnan, J., A common Lyapunov function for stable LTI systems with commuting A-matrices, IEEE Trans. Automat. Control, 39, 2469-2471 (1994) · Zbl 0825.93668
[10] Shorten, R. N.; Narendra, K. S., On the stability and existence of common Lyapunov functions for stable linear switching systems, (Proc. 37th Conf. Decision and Control (1998)), 3723-3724
[11] Ye, H.; Michel, A. N.; Hou, L., Stability theory for hybrid dynamical systems, IEEE Trans. Automat. Control, 43, 461-474 (1998) · Zbl 0905.93024
[12] Branicky, M. S., Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, IEEE Trans. Automat. Control, 43, 475-482 (1998) · Zbl 0904.93036
[13] Peleties, P.; DeCarlo, R. A., Asymptotic stability of m-switched systems using Lyapunov-like functions, (Proc. American Control Conference (1991)), 1679-1684
[14] Petterson, S.; Lennartson, B., Stability and robustness for hybrid systems, (Proc. 35th IEEE Conf. Decision and Control. Proc. 35th IEEE Conf. Decision and Control, Kobe, Japan (1996)), 1202-1207
[15] Xu, X.; Antsaklis, P. J., Design of stabilizing control laws for second-order switched systems, (Proc. 14th IFAC World Congress, vol. C. Proc. 14th IFAC World Congress, vol. C, Beijing, PR China (1999)) · Zbl 0948.93013
[16] Hu, B.; Xu, X.; Antsaklis, P. J.; Michel, A. N., Robust stabilizing control laws for a class of second-order switched systems, Systems Control Lett., 38, 197-207 (1999) · Zbl 0948.93013
[17] Hespanha, J. P.; Morse, A. S., Stability of switched systems with average dwell-time, (Proc. 38th Conf. Decision and Control. Proc. 38th Conf. Decision and Control, Phoenix, AZ, USA (1999)), 2655-2660 · Zbl 0108.23602
[18] Wicks, M. A.; Peleties, P.; DeCarlo, R. A., Switched controller synthesis for the quadratic stabilization of a pair of unstable linear systems, Eur. J. Control, 4, 140-147 (1998) · Zbl 0910.93062
[19] Li, Z. G.; Wen, C. Y.; Soh, Y. C., Stabilization of a class of switched systems via designing switching laws, IEEE Trans. Automat. Control, 46, 665-670 (2001) · Zbl 1001.93065
[20] Hu, B.; Xu, X.; Antsaklis, P. J.; Michel, A. N., Robust stabilizing control laws for a class of second-order switched systems, Systems Control Lett., 38, 197-207 (1999) · Zbl 0948.93013
[21] Kaileth, T., Linear Systems (1980), Prentice Hall: Prentice Hall Englewood Cliffs, NJ · Zbl 0454.93001
[22] Chen, C.-T., Linear System Theory and Design (1999), Oxford Univ. Press: Oxford Univ. Press New York
[23] Wonham, W. M., Linear Multivariable Control: A Geometric Approach (1985), Springer-Verlag: Springer-Verlag New York · Zbl 0393.93024
[24] Zhao, Q.; Zheng, D., Stable and real-time scheduling of a class of hybrid dynamic systems, J. DEDS, 9, 45-64 (1999) · Zbl 0920.90078
[25] Schinkel, M.; Wang, Y.; Hunt, K., Stable and robust state feedback design for hybrid systems, (Proc. American Control Conference. Proc. American Control Conference, Chicago (2000)), 215-219
[26] Ishii, H.; Francis, B., Stabilization with control networks, (Control 2000. Control 2000, Cambridge UK (2000)) · Zbl 1011.93502
[27] Ishii, H.; Francis, B., Stabilizing a linear system by switching control with dwell time, (Proc. American Control Conference (2001)), 1876-1881
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