Stability of quantized time-delay nonlinear systems: A Lyapunov-Krasowskii- functional approach

Mathematics of Control, Signals, and Systems

Volumn 21, Issue 4, 2010, Pages 337-370

  De Persis, Claudio ^a   Mazenc, Frédéric ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b CNRS   (France)

Author keywords

Hysteresis; Nonlinear systems; Quantized systems; Switched systems; Time delay systems

Indexed keywords

ALLOWABLE DELAY; CONSTANT DELAYS; FUNCTIONAL APPROACH; FUNCTIONALS; LYAPUNOV; NONLINEAR CONTINUOUS-TIME SYSTEMS; QUANTIZATION DENSITY; QUANTIZED CONTROL; QUANTIZED FEEDBACK; QUANTIZED SYSTEMS; SWITCHED SYSTEM; TIME-DELAY SYSTEMS;

CONTROL THEORY; DELAY CONTROL SYSTEMS; HYSTERESIS; NONLINEAR SYSTEMS; SWITCHING SYSTEMS; TIME DELAY;

CONTINUOUS TIME SYSTEMS;

EID: 79952698986     PISSN: 09324194     EISSN: 1435568X     Source Type: Journal    
DOI: 10.1007/s00498-010-0048-1     Document Type: Article

References (21)

1. Ceragioli F, De Persis C (2007) Discontinuous stabilization of nonlinear systems: Quantized and switching control. Syst Control Lett 56:461-473 (Pubitemid 46783051)
2. De Persis C (2009) Robust stabilization of nonlinear systems by quantized and ternary control. Syst Control Lett 58(8):602-608
3. Elia N, Mitter SK (2001) Stabilization of linear systems with limited information. IEEE Trans Autom Control 46(9):1384-1400 (Pubitemid 32981642)
4. Fridman E, Dambrine M, Yeganefar N (2008) On input-to-state stability of systems with time-delay: a matrix inequalities approach. Automatica 44:2364-2369
5. Hayakawa T, Ishii H, Tsumura K (2006) Adaptive quantized control for nonlinear uncertain systems. In: Proceedings of 2006 American control conference, Minneapolis, MN, USA
6. Hahn W (1967) Stability of motion. Springer, Berlin
7. Isidori A (1999) Nonlinear control systems, vol 2. Springer, London
8. Jankovic M (2001) Control-Lyapunov-Razumikhin functions and robust stabilization of time delay systems. IEEE Trans Autom Control 46(7):1048-1060 (Pubitemid 32732628)
9. Karafyllis I (2006) Lyapunov theorems for systems described by retarded functional differential equations. Nonlinear Anal Theory Methods Appl 64(3):590-617 (Pubitemid 41772929)
10. Khalil HK (1996) Nonlinear systems, 2nd edn. Prentice Hall, Upper Saddle River
11. Krasowskii NN (1963) Stability of motion. Stanford University Press, Stanford
12. Liberzon D (2003) Hybrid feedback stabilization of systems with quantized signals. Automatica 39(9):1543-1554
13. Liberzon D (2006) Quantization, time delays, and nonlinear stabilization. IEEE Trans Autom Control 51(7):1190-1195 (Pubitemid 44070139)
14. Mazenc F, Bliman P-A (2006) Backstepping design for time-delay nonlinear systems. IEEE Trans Autom Control51:149-154 (Pubitemid 43137944)
15. Mazenc F, Mondié S, Francisco R (2004) Global asymptotic stabilization of feedforward systems with delay in the input. IEEE Trans Autom Control 49(5):844-850
16. Michiels W, Sepulchre R, Roose R (2001) Stability of perturbed delay differential equations and stabilization ofnonlinearcascade systems. SIAM J Control Optim 40(3):661-680
17. Mazenc F, Niculescu S (2001) Lyapunov stability analysis for nonlinear delay systems. Syst Control Lett 42(4):245-251 (Pubitemid 32663810)
18. Pepe P, Jiang ZP (2006) A Lyapunov-Krasovskii methodology for ISS and iISS of time-delay systems. Syst Control Lett 55(12):1006-1014 (Pubitemid 44572521)
19. Sontag ED (1989) A "universal" construction of Artstein's theorem on nonlinear stabilization. Syst Control Lett 13:117-123
20. Teel AR (1998) Connections between Razumikhin-type theorems and the ISS nonlinear small-gain theorem. IEEE Trans Autom Control 43(7):960-964 (Pubitemid 128737728)
21. Teel AR, Praly L (1996) Tool for semi-global stabilization by partial state and output feedback. SIAM J Control Optim 33:1443-1488