Numerical verification of local input-to-state stability for large networks

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2007, Pages 4471-4476

  Dashkovskiy, Sergey N ^a   Rüffer, Björn S ^a   Wirth, Fabian R ^b  

^a UNIVERSITY OF BREMEN   (Germany)

^b UNIVERSITY OF WÜRZBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL ANALYSIS; VERIFICATION;

LOCALLY INPUT-TO-STATE STABLE (LISS); QUANTITATIVE RESULTS;

ASYMPTOTIC STABILITY;

EID: 62749179721     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2007.4434626     Document Type: Conference Paper

References (12)

1. S. Dashkovskiy, B. Rüffer, and F. Wirth. A small-gain type stability criterion for large scale networks of ISS systems. In Proc. of 44th IEEE Conference on Decision and Control and European Control Conference CDC/ECC 2005, pages 5633 - 5638, Seville, Spain, December 2005.
2. S. Dashkovskiy, B. Rüffer, and F. Wirth. Construction of ISS Lyapunov functions for networks. Berichte aus der Technomathematik 06-06, Zentrum für Technomathematik, Bremen, Germany, 2006. www.math.uni-bremen. de/zetem/reports/reports-pdf/report0606.pdf.
3. S. Dashkovskiy, B. Rüffer, and F. Wirth. An ISS Lyapunov function for networks of ISS systems. In Proc. 17th Int. Symp. Math. Theory of Networks and Systems, MTNS2006, pages 77-82, Kyoto, Japan, July 24-28 2006.
4. S. Dashkovskiy, B. Rüffer, and F. Wirth. An ISS small-gain theorem for general networks. Math. Control Signals Systems, 19:93-122, 2007.
5. S. Dashkovskiy, B. Rüffer, and F. Wirth. A Lyapunov ISS small gain theorem for strongly connected networks. In Proc. 7th IFAC Symposium on Nonlinear Control Systems, NOLCOS2007, pages 283-288, Pretoria, South Africa, August 2007.
6. S. Dashkovskiy, B. Rüffer, and F. Wirth. Stability of autonomous logistic processes via small gain criteria. In Proc. International Conference on Dynamics in Logistics, Bremen, August 2007. submitted.
7. B. Curtis Eaves. Homotopies for computation of fixed points. Math. Programming, 3:1-22, 1972.
8. Z.-P. Jiang, I. M. Y. Mareels, and Y. Wang. A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems. Automatica J. IFAC, 32(8):1211-1215, 1996.
9. Z.-P. Jiang, A. R. Teel, and L. Praly. Small-gain theorem for ISS systems and applications. Math. Control Signals Systems, 7(2):95-120, 1994.
10. B. S. Rüffer. Monotone Systems, Graphs, and Stability of Large-Scale Interconnected Systems. Dissertation, Dep. of Mathematics, University of Bremen, Germany, August 2007.
11. Eduardo D. Sontag. Smooth stabilization implies coprime factorization. IEEE Trans. Automat. Control, 34(4):435-443, 1989.
12. Eduardo D. Sontag and Yuan Wang. New characterizations of input-to-state stability. IEEE Trans. Automat. Control, 41(9):1283-1294, 1996.