A small-gain type stability criterion for large scale networks of ISS systems

Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

Volumn 2005, Issue , 2005, Pages 5633-5638

  Dashkovskiy, Sergey ^a   Rüffer, Björn Sebastian ^a   Wirth, Fabian R ^b  

^a UNIVERSITY OF BREMEN   (Germany)

^b NATIONAL UNIVERSITY OF IRELAND   (Ireland)

Author keywords

Gain matrix; Interconnected systems; ISS; Large scale systems; Small gain theorem; Stability

Indexed keywords

CONTROL THEORY; GAIN CONTROL; MATRIX ALGEBRA; NONLINEAR CONTROL SYSTEMS; SPECTRUM ANALYSIS; SYSTEM STABILITY;

GAIN MATRIX; ISS SYSTEMS; NONLINEAR GENERALIZATION; SMALL GAIN THEOREM;

LARGE SCALE SYSTEMS;

EID: 33847225203     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2005.1583060     Document Type: Conference Paper

References (12)

1. S. Dashkovskiy, B. Rüffer, and F. Wirth. An ISS small-gain theorem for general networks. Berichte aus der Technomathematik 05-05, Zentrum für Technomathematik, Bremen, Germany, 2005.
2. L. Grüne. Input-to-state dynamical stability and its Lyapunov function characterization. IEEE Trans. Automat. Control, 47(9): 1499-1504, 2002.
3. D. Hinrichsen and A. J. Pritchard. Mathematical Systems Theory I - Modelling, State Space Analysis, Stability and Robustness. Springer-Verlag, Berlin, 2005.
4. 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.
5. 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.
6. M. Karow, D. Hinrichsen, and A. Pritchard. Interconnected systems with uncertain couplings: explicit formulae for μ-values, spectral value sets and stability radii. Preprint, Institute of Mathematics, Technische Universität Berlin, 2005.
7. H. K. Khalil. Nonlinear Systems. Prentice-Hall, Inc., Upper Saddle River, NJ, 1996.
8. D. D. Šiljak. Large-scale dynamic systems. North-Holland Publishing Co., New York, 1979.
9. E. Sontag and A. Teel. Changing supply functions in input/state stable systems. IEEE Trans. Automat. Control, 40(8): 1476-1478, 1995.
10. E. D. Sontag. The ISS philosophy as a unifying framework for stability-like behavior. In Nonlinear control in the year 2000, Vol. 2 (Paris), volume 259 of Lecture Notes in Control and Inform. Sci., pages 443-467. Springer, London, 2001.
11. E. D. Sontag and Y. Wang. New characterizations of input-to-state stability. IEEE Trans. Automat. Control, 41(9): 1283-1294, 1996.
12. M. Vidyasagar. Input-output analysis of large-scale interconnected systems, volume 29 of Lecture Notes in Control and Information Sciences. Springer-Verlag, Berlin, 1981.