Measurement to error stability: A notion of partial detectability for nonlinear systems

Proceedings of the IEEE Conference on Decision and Control

Volumn 4, Issue , 2002, Pages 3946-3951

  Ingalls, Brian P ^a   Sontag, Eduardo D ^b   Wang, Yuan ^c  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b RUTGERS UNIVERSITY   (United States)

^c FLORIDA ATLANTIC UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CONTROL SYSTEM ANALYSIS; ERROR ANALYSIS; LYAPUNOV METHODS; NONLINEAR CONTROL SYSTEMS; SET THEORY;

INPUT TO OUTPUT STABILITY; INPUT TO STATE STABILITY; MEASUREMENT TO ERROR STABILITY; OUTPUT TO STATE STABILITY;

STABILITY CRITERIA;

EID: 0036997349     PISSN: 01912216     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (28)

1. F. H. Clarke, Yu. S. Ledyaev, R. J. Stern, and P. R. Wolenski, Nonsmooth Analysis and Control Theory, Springer, New York, 1998.
2. K. Deimling, Multivalued Differential Equations, Walter De Gruyter & Co., Berlin, 1992.
3. A. F. Filippov, Differential Equations with Discontinuous Righthand Sides, Kluwer Academic, Dordrecht, The Netherlands, 1988.
4. P. Hartman, Ordinary Differential Equations, John Wiley & Sons, New York, 1964.
5. B. Ingalls, E. D. Sontag, and Y. Wang, Generalizations of asymptotic gain characterizations of ISS to input-to-output stability, Proceedings of the AACC American Control Conference, Arlington, Virginia, 2001, pp. 2279-2284.
6. B. Ingalls and E. D. Sontag, A small-gain theorem with applications to input/output systems, incremental stability, detectability, and interconnections, to appear in Journal of the Franklin Institute.
7. B. Ingalls, E. D. Sontag, and Y. Wang, An infinite-time relaxation theorem for differential inclusions, to appear in Proceedings of the American Mathematical Society.
8. A. Isidori, Nonlinear Control Systems, Springer-Verlag, London, 3rd ed., 1995.
9. A. Isidori, Nonlinear Control Systems II, Springer-Verlag, London, 1999.
10. Z.-P. Jiang, A. Teel, and L. Praly, Small-gain theorem for ISS systems and applications, Mathematics of Control, Signals, and Systems, 7 (1994), pp. 95-120.
11. H. K. Khalil, Nonlinear Systems, Prentice-Hall, Upper Saddle River, NJ, second ed., 1996.
12. P. V. Kokotovic and M. Arcak, Constructive nonlinear control: progress in the 90's, Invited Plenary Talk, IFAC Congress, in Proc. 14th IFAC World Congress, the Plenary and Index Volume, pp. 49-77, Beijing, 1999.
13. M. Krichman, E. D. Sontag, and Y. Wang, Input-output-to-state stability, SIAM Journal on Control and Optimization, 39 (2001), pp. 1874-1928.
14. M. Krstić and H. Deng, Stabilization of Uncertain Nonlinear Systems, Springer-Verlag, London, 1998.
15. V. Lakshmikantham, S. Leela, and A. A. Martyuk, Practical Stability of Nonlinear Systems, World Scientific, New Jersey, 1990.
16. D. Liberzon, E. D. Sontag, and A. Morse, Output-input stability and minimum-phase nonlinear systems, to appear in IEEE Transactions on Automatic Control.
17. Y. Lin, E. D. Sontag, and Y. Wang, A smooth converse Lyapunov theorem for robust stability, SIAM Journal on Control and Optimization, 34 (1996), pp. 124-160.
18. ∞ control, Systems & Control Letters, 41 (2000), pp. 237-249.
19. E. D. Sontag, Smooth stabilization implies coprime factorization, IEEE Transactions on Automatic Control, 34 (1989), pp. 435-443.
20. E. D. Sontag, Comments on Integral Variants of ISS Systems and Control Letters, 34 (1998), pp. 93-100.
21. E. D. Sontag, The ISS philosophy as a unifying framework for stability-like behavior, in Nonlinear Control in the Year 2000, (Lecture Notes in Control and Information Sciences, A. Isidori, F. Lamnabhi-Lagarrigue, and W. Respondek, eds.), Springer-Verlag, Berlin, 2000, pp. 443-468.
22. E. D. Sontag and Y. Wang, Detectability of nonlinear systems, in Proceedings of the Conference on Information Sciences and Systems (CISS 96), Princeton, NJ, 1996, pp. 1031-1036.
23. E. D. Sontag and Y. Wang, Output-to-state stability and detectability of nonlinear systems, Systems & Control Letters, 29 (1997), pp. 279-290.
24. E. D. Sontag and Y. Wang, Notions of input to output stability, Systems & Control Letters, 38 (1999), pp. 351-359.
25. E. D. Sontag and Y. Wang, Lyapunov characterizations of input to output stability, SIAM Journal on Control and Optimization, 39 (2001), pp. 226-249.
26. A. R. Teel and L. Praly, A smooth Lyapunov function from a class-KL estimate involving two positive semi-definite functions, ESAIM: Control, Optimisation and Calculus of Variations, 5 (2000), pp. 313-368.
27. J. Tsinias, Input to state stability properties of nonlinear systems and applications to bounded feedback stabilization using saturation, ESAIM: Control, Optimisation and Calculus of Variations, 2 (1997), pp. 57-85.
28. V. I. Vorotnikov, Stability and stabilization of motion: Research approaches, results, distinctive characteristics, Automation and Remote Control, 54 (1993): pp. 339-397.