Analysis of input-to-state stability for discrete time nonlinear systems via dynamic programming

Automatica

Volumn 41, Issue 12, 2005, Pages 2055-2065

  Huang, Shoudong ^a   James, Matthew R ^b,d,e   Nešić, Dragan ^c,d,e   Dower, Peter M ^c  

^a UNIVERSITY OF TECHNOLOGY SYDNEY   (Australia)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^c UNIVERSITY OF MELBOURNE   (Australia)

^d IEEE   (Australia)

^e IEAust ^*  (Australia)

Author keywords

Disturbances; Dynamic programming; Input to state stability; Nonlinear systems; Stability analysis

Indexed keywords

DISTURBANCES; INPUT-TO-STATE STABILITY; NONLINEAR DISSIPATIVE SYSTEMS THEORY; STABILITY ANALYSIS;

DISCRETE TIME CONTROL SYSTEMS; DYNAMIC PROGRAMMING; OPTIMIZATION; PROBLEM SOLVING; TRANSIENTS;

NONLINEAR SYSTEMS;

EID: 27344457768     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2005.07.005     Document Type: Article

References (17)

1. D. Angeli A Lyapunov approach to incremental stability properties IEEE Transactions on Automatic Control 47 2002 410 422
2. I.J. Fialho, and T.T. Georgiou Worst case analysis of nonlinear systems IEEE Transactions on Automatic Control 44 6 1999 1180 1196
3. Gao, K. & Lin, Y. (2000). On equivalent notions of input-to-state stability for nonlinear discrete time systems. Proceedings of IASTED international conference on control and applications, pp. 81-87.
4. J.W. Helton, and M.R. James Extending H ∞ control to nonlinear systems: Control of nonlinear systems to achieve performance objectives 1999 SIAM Philadelphia
5. S. Huang, and M.R. James l ∞ -bounded robustness for nonlinear systems: Analysis and synthesis IEEE Transactions on Automatic Control 48 11 2003 1875 1891
6. Z.P. Jiang, and I.M.Y. Mareels A small gain control method for nonlinear cascaded systems with dynamic uncertainties IEEE Transactions on Automatic Control 42 1997 292 308
7. Z.P. Jiang, I.M.Y. Mareels, and Y. Wang A Lyapunov formulation of the nonlinear small gain theorem for interconnected ISS systems Automatica 32 1996 1211 1215
8. Z.P. Jiang, A.R. Teel, and L. Praly Small gain theorem for ISS systems and applications Mathematics of Control Signal and Systems 7 1994 95 120
9. Z.P. Jiang, and Y. Wang Input-to-state stability for discrete-time nonlinear systems Automatica 37 2001 857 869
10. Nešić, D., & Teel, A. R. (2001b). Backstepping on the Euler approximate model for stabilization of sampled-data nonlinear systems. Proceedings of the IEEE conference on decision and control, Orlando, Florida, pp. 1737-1742.
11. Nešić, D., & Teel, A. R. (2004). Stabilization of sampled-data nonlinear systems via backstepping on their Euler approximate model. Automatica, to appear.
12. E.D. Sontag Smooth stabilization implies coprime factorization IEEE Transactions on Automatic Control 34 1989 435 443
13. Sontag, E. D. (2000). The ISS philosophy as a unifying framework for stability-like behavior. In Isidori, A., Lamnabhi-Lagarrigue, F., Respondek, W. (Eds.), Nonlinear control in the year 2000, Vol. 2. Lecture Notes in Control and Information Sciences. Berlin: Springer, pp. 443-468.
14. E.D. Sontag, and Y. Wang On characterizations of the input-to-state stability property Systems and Control Letters 24 1995 351 359
15. E.D. Sontag, and Y. Wang New characterizations of input to state stability IEEE Transactions on Automatic Control 41 1996 1283 1294
16. E.D. Sontag, and Y. Wang Lyapunov characterizations of input to output stability SIAM Journal of Control and Optimization 39 2001 226 249
17. A.R. Teel A nonlinear small gain theorem for the analysis of control systems with saturation IEEE Transactions on Automatic Control 41 1996 1256 1270