Probabilistic sorting and stabilization of switched systems

Automatica

Volumn 45, Issue 3, 2009, Pages 776-782

  Ishii, Hideaki ^a   Tempo, Roberto ^b  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^b POLITECNICO DI TORINO   (Italy)

Author keywords

Common Lyapunov functions; Randomized algorithms; Switched systems

Indexed keywords

ALGORITHMS; CONTROL THEORY; DIFFERENTIAL EQUATIONS; FUNCTIONS; LINEAR SYSTEMS; LYAPUNOV FUNCTIONS; PROBABILITY DENSITY FUNCTION; SWITCHING SYSTEMS;

COMMON LYAPUNOV FUNCTIONS; DESIGN PROCEDURES; LAS VEGAS; LYAPUNOV; LYAPUNOV STABILITIES; RANDOMIZED ALGORITHMS; SWITCHED LINEAR SYSTEMS; SWITCHED SYSTEMS; SWITCHING RULES; SWITCHING SIGNALS; THIRD ORDERS;

TELECOMMUNICATION NETWORKS;

EID: 60449120470     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2008.10.016     Document Type: Article

References (17)

1. Alamo T., Tempo R., Ramírez D.R., and Camacho E.F. A new vertex result for robustness problems with interval matrix uncertainty. Systems & Control Letters 57 (2008) 474-481
2. Cheng D., Guo L., and Huang J. On quadratic Lyapunov functions. IEEE Transactions on Automatic Control 48 (2003) 885-890
3. Fujisaki Y., Dabbene F., and Tempo R. Probabilistic design of LPV control systems. Automatica 39 (2003) 1323-1337
4. Gurvits L., Shorten R., and Mason O. On the stability of switched positive linear systems. IEEE Transactions on Automatic Control 52 (2007) 1099-1103
5. Ishii H., Başar T., and Tempo R. Randomized algorithms for synthesis of switching rules for multimodal systems. IEEE Transactions on Automatic Control 50 (2005) 754-767
6. Knuth D.E. The art of computer programming. 2nd edition. Sorting and searching Vol. 3 (1998), Addison-Wesley, Reading, MA
7. Liberzon D. Switching in systems and control (2003), Birkhäuser, Boston
8. Liberzon D., and Tempo R. Common Lyapunov functions and gradient algorithms. IEEE Transactions on Automatic Control 49 (2004) 990-994
9. Mitzenmacher M., and Upfal E. Probability and computing: Randomized algorithms and probabilistic analysis (2005), Cambridge University Press
10. Motwani R., and Raghavan P. Randomized algorithms (1995), Cambridge University Press
11. Rugh W.J., and Shamma J.S. Research on gain scheduling. Automatica 36 (2000) 1401-1425
12. Shorten R.N., and Narendra K.S. Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a finite number of stable second order linear time-invariant systems. International Journal of Adaptive Control Signal Process 16 (2002) 709-728
13. Sun Z., and Ge S.S. Analysis and synthesis of switched linear control systems. Automatica 41 (2005) 181-195
14. Tempo R., and Ishii H. Monte Carlo and Las Vegas randomized algorithms for systems and control: An introduction. European Journal of Control 13 (2007) 189-203
15. Tempo R., Bai E.W., and Dabbene F. Probabilistic robustness analysis: Explicit bounds for the minimum number of samples. Systems & Control Letters 30 (1997) 237-242
16. Tempo R., Calafiore G., and Dabbene F. Randomized algorithms for analysis and control of uncertain systems (2005), Springer, London
17. Vidyasagar M. Statistical learning theory and randomized algorithms for control. IEEE Control Systems Magazine 18 6 (1998) 69-85