Open Access

A unified approach to stability analysis of switched linear descriptor systems under arbitrary switching

Boyd, S., El Ghaoui, L., Feron, E. and Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA.10.1137/1.9781611970777Search in Google Scholar

Branicky, M. S. (1998). Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, IEEE Transactions on Automatic Control 43(4): 475-482.10.1109/9.664150Search in Google Scholar

Cobb, D. (1983). Descriptor variable systems and optimal state regulation, IEEE Transactions on Automatic Control 28(5): 601-611.10.1109/TAC.1983.1103283Search in Google Scholar

DeCarlo, R., Branicky, M. S., Pettersson, S. and Lennartson, B. (2000). Perspectives and results on the stability and stabilizability of hybrid systems, Proceedings of the IEEE 88(7): 1069-1082.10.1109/5.871309Search in Google Scholar

Hespanha, J. P. and Morse, A. S. (2002). Switching between stabilizing controllers, Automatica 38(11): 1905-1917.10.1016/S0005-1098(02)00139-5Search in Google Scholar

Hu, B., Zhai, G. and Michel, A. N. (2002). Hybrid static output feedback stabilization of second-order linear time-invariant systems, Linear Algebra and Its Applications 351-352: 475-485.10.1016/S0024-3795(01)00471-2Search in Google Scholar

Ikeda, M., Lee, T. W. and Uezato, E. (2000). A strict LMI condition for H2 control of descriptor systems, Proceedings of the 39th IEEE Conference on Decision and Control, CDC 2000, Sydney, Australia, pp. 601-604.Search in Google Scholar

Ishida, J. Y. and Terra, M. H. (2001). On the Lyapunov theorem for descriptor systems, Proceedings of the 40th IEEE Conference on Decision and Control, CDC 2001, Orlando, FL, USA, pp. 2860-2864.Search in Google Scholar

Kaczorek, T. (2002). Polynomial approach to pole shifting to infinity in singular systems by feedbacks, Bulletin of the Polish Academy of Sciences: Technical Sciences 50(2): 134-144.Search in Google Scholar

Kaczorek, T. (2004). Infinite eigenvalue assignment by output feedback for singular systems, International Journal of Applied Mathematics and Computer Science 14(1): 19-23.Search in Google Scholar

Lewis, F. L. (1986). A survey of linear singular systems, Circuits Systems Signal Process 5(1): 3-36.10.1007/BF01600184Search in Google Scholar

Liberzon, D. (2003). Switching in Systems and Control, Birkhäuser, Boston, MA.10.1007/978-1-4612-0017-8Search in Google Scholar

Liberzon, D., Hespanha, J. P. and Morse, A. S. (1999). Stability of switched systems: A Lie-algebraic condition, Systems & Control Letters 37(3): 117-122.10.1016/S0167-6911(99)00012-2Search in Google Scholar

Liberzon, D. and Morse, A. S. (1999). Basic problems in stability and design of switched systems, IEEE Control Systems Magazine 19(5): 59-70.10.1109/37.793443Search in Google Scholar

Masubuchi, I., Kamitane, Y., Ohara, A. and Suda, N. (1997). H control for descriptor systems: A matrix inequalities approach, Automatica 33(4): 669-673.10.1016/S0005-1098(96)00193-8Search in Google Scholar

Narendra, K. S. and Balakrishnan, J. (1994). A common Lyapunov function for stable LTI systems with commuting A-matrices, IEEE Transactions on Automatic Control 39(12): 2469-2471.10.1109/9.362846Search in Google Scholar

Sun, Z. and Ge, S. S. (2005a) Analysis and synthesis of switched linear control systems, Automatica 41(2): 181-195.10.1016/j.automatica.2004.09.015Search in Google Scholar

Sun, Z. and Ge, S. S. (2005b). Switched Linear Systems: Control and Design, Springer, London.10.1007/1-84628-131-8Search in Google Scholar

Takaba, K., Morihara, N. and Katayama, T. (1995). A generalized Lyapunov theorem for descriptor systems, Systems & Control Letters 24(1): 49-51.10.1016/0167-6911(94)00041-SSearch in Google Scholar

Uezato, E. and Ikeda, M. (1999). Strict LMI conditions for stability, robust stabilization, and H control of descriptor systems, Proceedings of the 38th IEEE Conference on Decision and Control, CDC 1999, Phoenix, AZ, USA, pp. 4092-4097.Search in Google Scholar

Xu, S. and Yang, C. (1999). Stabilization of discrete-time singular systems: A matrix inequalities approach, Automatica 35(9): 1613-1617.10.1016/S0005-1098(99)00061-8Search in Google Scholar

Zhai, G., Hu, B., Yasuda, K. and Michel, A. N. (2001). Disturbance attenuation properties of time-controlled switched systems, Journal of The Franklin Institute 338(7): 765-779.10.1016/S0016-0032(01)00030-8Search in Google Scholar

Zhai, G., Hu, B., Yasuda, K. and Michel, A. N. (2002). Stability and L2 gain analysis of discrete-time switched systems, Transactions of the Institute of Systems, Control and Information Engineers 15(3): 117-125.10.5687/iscie.15.117Search in Google Scholar

Zhai, G., Liu, D., Imae, J. and Kobayashi, T. (2006). Lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems, IEEE Transactions on Circuits and Systems II 53(2): 152-156.10.1109/TCSII.2005.856033Search in Google Scholar

Zhai, G. and Xu, X. (2009). A unified approach to analysis of switched linear descriptor systems under arbitrary switching, Proceedings of the 48th IEEE Conference on Decision and Control, CDC 2009, Shanghai, China, pp. 3897-3902.Search in Google Scholar

Zhai, G., Kou, R., Imae, J. and Kobayashi, T. (2009a). Stability analysis and design for switched descriptor systems, International Journal of Control, Automation, and Systems 7(3): 349-355.10.1007/s12555-009-0303-8Search in Google Scholar

Zhai, G., Xu, X., Imae, J. and Kobayashi, T. (2009b). Qualitative analysis of switched discrete-time descriptor systems, International Journal of Control, Automation, and Systems 7(4): 512-519.10.1007/s12555-009-0402-6Search in Google Scholar

ISSN:
1641-876X
Language:
English
Publication timeframe:
4 times per year
Journal Subjects:
Mathematics, Applied Mathematics