Lyapunov-ISS cyclic-small-gain in hybrid dynamical networks

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 43, Issue 14, 2010, Pages 813-818

  Liu, Tengfei ^a   Jiang, Zhong Ping ^b   Hill, David J ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b POLYTECHNIC UNIVERSITY   (United States)

Author keywords

Cyclic small gain; Hybrid systems; Lyapunov formulation

Indexed keywords

HYBRID SYSTEMS; NONLINEAR CONTROL SYSTEMS;

CONTINUOUS-TIME; DISCRETE TIME; HYBRID DYNAMICAL; INPUT TO STATE STABLE; SAMPLING TIME; SMALL GAIN; SMALL GAIN THEOREM; SMALL-GAIN CONDITION;

CONTINUOUS TIME SYSTEMS;

EID: 80051735451     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20100901-3-IT-2016.00016     Document Type: Conference Paper

References (32)

1. Cai, C., & Teel, A. R. (2009). Characterizations of input-to-state stability for hybrid systems. Systems & Control Letters, 58, 47-53.
2. Chen, W.-H. & Zheng, W. X. (2009). Input-to-state stability and integral input-to-state stability of nonlinear impulsive systems with delays. Automatica, 45(6), 1481-1488.
3. Dashkovskiy, S. & Kosmykov, M. (2009). Stability of networks of hybrid ISS systems. In Proceedings of Proceedings of Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (pp. 3870-3875).
4. Dashkovskiy, S., Rüffer, B. S., & Wirth, F. R. (2006). On the construction of ISS Lyapunov functions of networks of ISS systems. In Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (pp. 77-82).
5. Dashkovskiy, S., Rüffer, B. S., & Wirth, F. R. (2007). An ISS small-gain theorem for general networks. Mathematics of Control, Signals and Systems, 19, 93-122. (Pubitemid 46784529)
6. Hespanha, J. P., Liberzon, D., & Teel, A. R. (2008). Lyapunov conditions for input-to-state stability of impulsive systems. Automatica, 44, 2735-2744.
7. Hill, D. J. (1991). A generalization of the small-gain theorem for nonlinear feedback systems. Automatica, 27(6), 1043-1045.
8. Jiang, Z.-P., Lin, Y., & Wang, Y. (2008). Nonlinear small-gain theorems for discrete-time large-scale systems. In Proceedings of the 27th Chinese Control Conference (pp. 704-708).
9. Jiang, Z.-P., Mareels, I. M. Y., & Wang, Y. (1996). A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems. Automatica, 32(8), 1211-1215. (Pubitemid 126363671)
10. Jiang, Z.-P., Teel, A. R., & Praly, L. (1994). Small-gain theorem for ISS systems and applications. Mathematics of Control, Signals and Systems, 7, 95-120.
11. Jiang, Z.-P., & Wang, Y. (2001). Input-to-state stability for discrete-time nonlinear systems. Automatica, 37, 857-869. (Pubitemid 32426067)
12. Jiang, Z.-P., & Wang, Y. (2008). A generalization of the nonlinear small-gain theorem for large-scale complex systems. In Proceedings of the 7th World Congress on Intelligent Control and Automation (pp. 1188-1193).
13. Karafyllis, I., & Jiang, Z.-P. (2007). A small-gain theorem for a wide class of feedback systems with control applications. SIAM J. Control and Optimization, 46(4), 1483-1517.
14. Karafyllis, I., & Jiang, Z.-P. (2009). A vector small-gain theorem for general nonlinear control systems. In Proceedings of Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (pp. 7997-8001).
15. Karafyllis, I., Kravaris, C., Syrou, L., & Lyberatos, G. (2008). A vector Lyapunov function characterization of input-to-state stability with application to robust global stabilization of the chemostat. European Journal of Control, 14(1), 47-61.
16. Khalil, H. K. (2002). Nonlinear Systems (3rd Ed.). NJ: Prentice-Hall.
17. Laila, D. S., & Nešić, D. (2003). Lyapunov based small-gain theorem for parameterized discrete-time interconnected ISS systems. IEEE Trans. Automatic Control, 48, 1783-1788.
18. Lakshmikantham, V., & Leela, S. (1969). Differential and Integral inequalities: Theory and Applications. Volume I-Ordinary Differential Equations. New York: Academic Press.
19. Liberzon, D., & Nešić, D. (2006). Stability analysis of hybrid systems via small-gain theorems. In Proceedings of the 9th International Workshop on Hybrid Systems: Computation and Control (pp. 421-435). (Pubitemid 44019602)
20. J. P. Hespanha and A. Tiwari (Eds.). Lecture Notes in Computer Science, 3927, Berlin: Springer.
21. Liberzon, D., & Nešić, D. (2007). Input-to-state stabilization of linear systems with quantized state measurements. IEEE Trans. Automatic Control, 52(5), 767-781. (Pubitemid 46796064)
22. Lin, Y., Sontag, E. D., & Wang, Y. (1996). A smooth converse Lyapunov theorem for robust stability. SIAM Journal on Control and Optimization, 34, 124-160. (Pubitemid 126562693)
23. Liu, T., Hill, D. J., & Jiang, Z.-P. (2009). Lyapunov formulation of ISS cyclic-small-gain in dynamical networks. Automatica (accepted).
24. Mareels, I. M. Y., & Hill, D. J. (1992). Monotone stability of nonlinear feedback systems. Journal of Mathematical Systems, Estimation, and Control, 2(3), 275-291.
25. Nešić, D., & Teel, A. R. (2008). A Lyapunov-based small-gain theorem for hybrid ISS systems. In Proceedings of the 47th IEEE Conference on Decision and Control (pp. 3380-3385).
26. Rüffer, B. S. (2007). Monotone Systems, Graphs, and Stability of Large-Scale Interconnected Systems. Dissertation, University of Bremen, Germany. Available online: http://nbn-resolving.de/urn:nbn:de:gbv:46-diss000109058.
27. Sontag, E. D. (1989). Smooth stabilization implied coprime factorization. IEEE Trans. Automatic Control, 34, 435-443.
28. Sontag, E. D. (1990). Further facts about input to state stabilization. IEEE Trans. Automatic Control, 35, 473-476.
29. Sontag, E. D., & Wang, Y. (1995). On characterizations of the input-to-state stability property. System & Control Letters, 24, 351-359.
30. Sontag, E. D., & Wang, Y. (1996). New characterizations of input-to-state stability. IEEE Trans. Automatic Control, 41(9), 1283-1294. (Pubitemid 126768503)
31. Teel, A. R. (1996). A nonlinear small gain theorem for the analysis of control systems with saturation. IEEE Trans. Automatic Control, 41(9), 1256-1270. (Pubitemid 126768501)
32. Teel, A. R. (2003). Private communications.