Necessary conditions for global asymptotic stability of networks of iISS systems

Mathematics of Control, Signals, and Systems

Volumn 24, Issue 1-2, 2012, Pages 55-74

  Ito, Hiroshi ^a  

^a KYUSHU INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Dissipation inequalities; Dynamical networks; Integral input to state stability; Large scale nonlinear systems

Indexed keywords

ARBITRARY NUMBER; CONCISE REPRESENTATIONS; DISSIPATION INEQUALITY; DYNAMICAL NETWORKS; GLOBAL ASYMPTOTIC STABILITY; INPUT TO STATE STABLE; INTEGRAL INPUT-TO-STATE STABILITY; INTEGRAL INPUT-TO-STATE STABLES; LARGE-SCALE NONLINEAR SYSTEMS; NON-TRIVIAL; SMALL GAIN;

CONTROL; SIGNAL PROCESSING;

DYNAMICAL SYSTEMS;

EID: 84859102891     PISSN: 09324194     EISSN: 1435568X     Source Type: Journal    
DOI: 10.1007/s00498-012-0077-z     Document Type: Article

References (23)

1. D Angeli A Astolfi 2007 A tight small gain theorem for not necessarily ISS systems Syst Control Lett 56 87 91 2281486 10.1016/j.sysconle.2006.08.003 1120.93358 (Pubitemid 44750261)
2. D Angeli ED Sontag Y Wang 2000 A characterization of integral input-to-state stability IEEE Trans Autom. Control 45 1082 1097 1778368 10.1109/9.863594 0979.93106
3. M Araki 1975 Application of M-matrices to the stability problems of composite dynamical systems J Math Anal Appl 52 309 321 382793 10.1016/0022-247X(75)90099-2 0324.34045
4. Chartrand G, Lesniak L, Zhang P (2010) Graphs and digraphs, 5th edn. Chapman and Hall/CRC, Boca Raton
5. S Dashkovskiy B Rüffer F Wirth 2007 An ISS small-gain theorem for general networks Math Contr Signals Syst 19 93 122 10.1007/s00498-007-0014-8 1125.93062 (Pubitemid 46784529)
6. S Dashkovskiy B Rüffer F Wirth 2010 Small gain theorems for large scale systems and construction of ISS Lyapunov functions SIAM J Control Optim 48 4089 4118 2645475 10.1137/090746483 1202.93008
7. H Ito 2006 State-dependent scaling problems and stability of interconnected iISS and ISS systems IEEE Trans Autom Control 51 1626 1643 10.1109/TAC.2006.882930 (Pubitemid 44593670)
8. H Ito 2010 A Lyapunov approach to cascade interconnection of integral input-to-state stable systems IEEE Trans Automat Control 55 702 708 2654836 10.1109/TAC.2009.2037457
9. Ito H (2010) Construction of Lyapunov functions for networks of iISS systems: an explicit solution for a cyclic structure. In: Proceedings of the 2010 American control conference, Baltimore, USA, pp 196-201
10. Ito H, Dashkovskiy S, Wirth F (2009) On a small gain theorem for networks of iISS systems. In: Proceedings of the 48th IEEE conf decision contr, Shanghai, China, pp 4210-4215
11. H Ito ZP Jiang 2009 Necessary and sufficient small gain conditions for integral input-to-state stable systems: a Lyapunov perspective IEEE Trans Autom Control 54 2389 2404 2562842 10.1109/TAC.2009.2028980
12. Ito H, Jiang ZP, Dashkovskiy S, Rüffer B (2011) A small-gain theorem and construction of sum-type Lyapunov functions for networks of iISS systems. In: Proceedings of the 2011 American control conference San Francisco, USA, pp 1971-1977
13. ZP Jiang AR Teel L Praly 1994 Small-gain theorem for ISS systems and applications Math Control Signals Syst 7 95 120 1359023 10.1007/BF01211469 0836.93054
14. Jiang ZP, Wang Y (2008) A generalization of the nonlinear small-gain theorem for large-scale complex systems. In: Proceedings of the 2008 world congress on intelligent control and automation, Chongqing, China, pp 1188-1193
15. Lakshmikantham V, Matrosov VM, Sivasundaram S (1991) Vector Lyapunov functions and stability analysis of nonlinear systems. Kluwer, Dordrecht
16. Michel AN, Miller RK (1977) Qualitative analysis of large scale dynamical systems. Academic Press, New York
17. BS Rüffer CM Kellett SR Weller 2010 Connection between cooperative positive systems and integral input-to-state stability of large-scale systems Automatica 46 1019 1027 10.1016/j.automatica.2010.03.012 1192.93108
18. NR Sandell P Varaiya M Athans MG Safonov 1978 Survey of decentralized control methods for large scale systems IEEE Trans Autom Control 23 108 128 490108 10.1109/TAC.1978.1101704 0385.93001 (Pubitemid 8595795)
19. Šiljak DD (1978) Large-scale dynamic systems: stability and structure. North-Holland, New York
20. ED Sontag 1989 Smooth stabilization implies coprime factorization IEEE Trans Autom Control 34 435 443 987806 10.1109/9.28018 0682.93045
21. ED Sontag 1998 Comments on integral variants of ISS Syst Control Lett 34 93 100 1629012 10.1016/S0167-6911(98)00003-6 0902.93062 (Pubitemid 128449958)
22. ED Sontag Y Wang 1995 On characterizations of input-to-state stability property Syst Control Lett 24 351 359 1325675 10.1016/0167-6911(94)00050-6 0877.93121
23. A Teel 1996 A nonlinear small gain theorem for the analysis of control systems with saturation IEEE Trans Autom Control 41 1256 1270 1409471 10.1109/9.536496 0863.93073 (Pubitemid 126768501)