Stabilisation and L2-gain analysis for a class of uncertain switched non-linear systems

International Journal of Systems Science

Volumn 40, Issue 10, 2009, Pages 1077-1085

  Wang, Min ^a   Zhao, Jun ^a,b   Dimirovski, Georgi M ^c  

^a KEY LABORATORY OF INTEGRATED AUTOMATION OF PROCESS INDUSTRY   (China)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^c DOGUS UNIVERSITY   (Turkey)

Author keywords

Average dwell time method; Exponential stability; H infinity control; L2 gain; Piecewise Lyapunov function; Switched non linear cascade systems; Switching systems

Indexed keywords

AVERAGE DWELL-TIME METHOD; EXPONENTIAL STABILITY; H-INFINITY CONTROL; L2-GAIN; PIECEWISE LYAPUNOV FUNCTION; SWITCHED NON-LINEAR CASCADE SYSTEMS;

CASCADE CONTROL SYSTEMS; DIFFERENTIAL EQUATIONS; FEEDBACK; LINEAR SYSTEMS; LYAPUNOV FUNCTIONS; MULTIVARIABLE CONTROL SYSTEMS; NONLINEAR SYSTEMS; SWITCHING SYSTEMS; SYSTEM STABILITY; UNCERTAINTY ANALYSIS;

CONTROL SYSTEM STABILITY;

EID: 70449087351     PISSN: 00207721     EISSN: 14645319     Source Type: Journal    
DOI: 10.1080/00207720902974686     Document Type: Article

References (23)

1. Branicky, M.S. (1998), 'Multiple Lyapunov Functions and Other Analysis Tools for Switched Hybrid Systems', IEEE Transactions on Automatic Control, 43, 475-482.
2. Cheng, D., Guo, L., and Huang, J. (2003), 'On Quadratic Lyapunov Functions', IEEE Transactions on Automatic Control, 48, 885-890.
3. Cheng, D. (2004), 'Stabilization of Planar Switched Systems', System & Control Letters, 51, 79-88.
4. Hespanha, J.P., and Morse, A.S. (1999), 'Stability of Switched Systems With Average Dwell-time', in Proceedings of the Conference on Decision and Control, pp. 2655-2660.
5. Hu, B., Xu, X., Michel, A.N. and Antsaklis, P.J. (1999), 'Stability Analysis for a Class of Nonlinear Switched Systems', in Proceedings of the Conference on Decision and Control, pp. 4374-4379. (Pubitemid 30574885)
6. Khargonekar, P.P., Petersen, I.R., and Zhou, K. (2001), 'Robust Stabilization of Uncertain Linear Systems: Quadratic Stabilizablity and H1 Control Theory', IEEE Transactions on Automatic Control, 35, 356-361.
7. Liberzon, D., and Morse, A.S. (1999), 'Basic Problems in Stability and Design of Switched Systems', IEEE Control Systems Magazine, 19, 59-70. (Pubitemid 30505850)
8. Liberzon, D., Hespanha, H.J.P., and Morse, A.S. (1999), 'Stability of Switched Systems: A Lie-algebraic', Condition, System & Control Letters, 37, 117-122.
9. Liberzon, D. (2003), Switching in Systems and Control, Boston: Brikhauser.
10. Peleties, P., and Decarlo, R.A. (1999), 'Asymptotic Stability of m-Switched Systems Using Lyapunov-like Functions', in Proceedings of the American Control Conference, pp. 1679-1684.
11. Petersen, I.R. (1987), 'A Stabilization Algorithm for a Class of Uncertain Linear Systems', System & Control Letters, 8, 351-357.
12. Pettersson, S. (1999), Analysis and Design of Hybrid Systems, Göteborg, Sweden: Chalmers Reproservice.
13. Pettersson, S., and Lennartson, B. (2001), 'Stabilization of Hybrid Systems Using a Min-projection Strategy', in Proceedings of the American Control Conference, pp. 223-228.
14. Sun, X., Zhao, J., and Hill, D.J. (2006), 'Stability and L2-gain Analysis for Switched Delay Systems: A Delay-dependent Method', Automatica, 42, 1769-11744
15. Wang, R., Jin, G., and Zhao, J. (2007), 'Roust Fault-tolerant Control for a Class of Switched Nonlinear Systems in Lower Triangular Form', Asian Journal of Control, 9, 68-72.
16. Wang, R., and Zhao., J. (2007), 'Guaranteed Cost Control for a Class of Uncertain Switched Delay Systems: An Average Dwell-time Method', Cybernetics and Systems, 38, 105-122. (Pubitemid 46277635)
17. Wicks, W.A., Peleties, P., and DeCarlo, R.A. (1998), 'Switched Controller Synthesis for the Quadratic Stabilization of a Pair of Unstable Linear Systems', European Journal of Control, 4, 140-147.
18. Zefran, M., Bullo, F., and Stein, M. (2001), 'A Notion of Passivity for Hybrid Systems', in Proceedings of the Conference on Decision and Control, pp. 768-773.
19. Zhai, G., Hu, B., Yasuda, K., and Michel, A.N. (2000), 'Stability Analysis of Switched Systems With Stable and Unstable Subsystems: An Average Dwell Time Approach', in Proceedings of the American Control Conference, pp. 200-204.
20. 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, 765-779.
21. Zhai, G. (2001), 'Quadratic Stabilizability of Discrete-time Switched Systems Via State and Output Feedback', in Proceedings of the Conference on Decision and Control, pp. 2165-2166.
22. Zhao, J., and Hill, D.J. (2008), 'On Stability, and L2-gain and H1 Control for Switched Systems', Automatica, 44, 1220-1232.
23. Zhao, J., and Dimirovski, G.M. (2004), 'Quadratic Stability of a Class of Switched Nonlinear Systems', IEEE Transactions on Automatic Control, 49, 574-578.