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

 Access to full text

 Full (PDF)

1. Boyd, S., El Ghaoui, L., Feron, E. and Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA. Zbl0816.93004
2. 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. Zbl0904.93036
3. Cobb, D. (1983). Descriptor variable systems and optimal state regulation, IEEE Transactions on Automatic Control 28(5): 601-611. Zbl0522.93036
4. 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. 
5. Hespanha, J.P. and Morse, A.S. (2002). Switching between stabilizing controllers, Automatica 38(11): 1905-1917. Zbl1011.93533
6. Hu, B., Zhai, G. and Michel, A.N. (2002). Hybrid static output feedback stabilization of second-order linear timeinvariant systems, Linear Algebra and Its Applications 351-352: 475-485. Zbl1007.93061
7. 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. 
8. 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. 
9. 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. 
10. Kaczorek, T. (2004). Infinite eigenvalue assignment by output feedback for singular systems, International Journal of Applied Mathematics and Computer Science 14(1): 19-23. Zbl1171.93331
11. Lewis, F.L. (1986). A survey of linear singular systems, Circuits Systems Signal Process 5(1): 3-36. Zbl0613.93029
12. Liberzon, D. (2003). Switching in Systems and Control, Birkhäuser, Boston, MA. Zbl1036.93001
13. 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. Zbl0948.93048
14. Liberzon, D. and Morse, A.S. (1999). Basic problems in stability and design of switched systems, IEEE Control Systems Magazine 19(5): 59-70. 
15. Masubuchi, I., Kamitane, Y., Ohara, A. and Suda, N. (1997). $H_{\infty }$ control for descriptor systems: A matrix inequalities approach, Automatica 33(4): 669-673. Zbl0881.93024
16. 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. Zbl0825.93668
17. Sun, Z. and Ge, S.S. (2005a) Analysis and synthesis of switched linear control systems, Automatica 41(2): 181-195. Zbl1074.93025
18. Sun, Z. and Ge, S.S. (2005b). Switched Linear Systems: Control and Design, Springer, London. Zbl1075.93001
19. Takaba, K., Morihara, N. and Katayama, T. (1995). A generalized Lyapunov theorem for descriptor systems, Systems & Control Letters 24(1): 49-51. Zbl0883.93035
20. Uezato, E. and Ikeda, M. (1999). Strict LMI conditions for stability, robust stabilization, and $H_{\infty }$ control of descriptor systems, Proceedings of the 38th IEEE Conference on Decision and Control, CDC 1999, Phoenix, AZ, USA, pp. 4092-4097. 
21. Xu, S. and Yang, C. (1999). Stabilization of discrete-time singular systems: A matrix inequalities approach, Automatica 35(9): 1613-1617. Zbl0959.93048
22. 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. Zbl1022.93017
23. 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. 
24. 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. 
25. 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. 
26. 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. 
27. 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. 

1. Stanisław Bańka, Paweł Dworak, Krzysztof Jaroszewski, Linear adaptive structure for control of a nonlinear MIMO dynamic plant
2. Stanisław Bańka, Paweł Dworak, Krzysztof Jaroszewski, Design of a multivariable neural controller for control of a nonlinear MIMO plant