New converse lyapunov theorems and related results on exponential stability

Mathematics of Control, Signals, and Systems

Volumn 11, Issue 1, 1997, Pages 79-100

  Corless, Martin ^a   Glielmo, Luigi ^b  

^a Purdue University   (United States)

^b UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

Cascade systems; Converse results; Exponential stability; Linear systems; Linearization techniques; Lyapunov; Nonlinear systems; Parametrized systems

Indexed keywords

CASCADE CONTROL SYSTEMS; CONVERGENCE OF NUMERICAL METHODS; FUNCTION EVALUATION; LINEAR CONTROL SYSTEMS; LINEARIZATION; LYAPUNOV METHODS; NONLINEAR CONTROL SYSTEMS;

EXPONENTIAL STABILITY; PARAMETRIZED SYSTEMS;

SYSTEM STABILITY;

EID: 0031650123     PISSN: 09324194     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02741886     Document Type: Article

References (18)

1. R. G. Bartle, The Elements of Real Analysis, 2nd edition, Wiley: New York, 1976.
2. E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill: New York, 1955.
3. M. Corless and L. Glielmo, On the exponential stability of singularly perturbed systems, SIAM J. Control. Optim., 30(6) (1992).
4. M. Corless and G. Leitmann, Controller design for uncertain systems via Lyapunov functions, Proc. Amer. Control. Conf, Boston, MA, 1988.
5. R. DeCarlo, Linear Systems: A State Variable Approach with Numerical Implementation, Prentice-Hall: Englewood Cliffs, NJ, 1989.
6. J. Dieudonné, Foundations of Modern Analysis, Academic Press: New York, 1969.
7. G. H. Golub and C. F. Van Loan, Matrix Computations, 2nd edition, Johns Hopkins University Press, Baltimore, MD, 1989.
8. T. H. Gronwall, Note on the derivatives with respect to a parameter of the solutions of a system of differential equations, Ann. of Math., 20 (1918), 292-296.
9. W. Hahn, Stability of Motion, Springer-Verlag: Berlin, 1967.
10. R. E. Kalman and J. E. Bertram, Control system analysis and design via the "second method" of Lyapunov, I: continuous-time systems, ASME J. Basic Engr., 82 (1960), 371-393.
11. H. K. Khalil, Nonlinear Systems, 2nd edition, Macmillan: New York, 1996.
12. V. Lakshmikantham and S. Leela, Differential and Integral Inequalities, Vol. 1, Academic Press: New York, 1969.
13. Y. Lin, E. D. Sontag, and Y. Wang, A smooth converse Lyapunov theorem for robust stability, SIAM J. Control. Optim., 34(1) (1996).
14. J. L. Massera, Converse theorems of Lyapunov's second method, Proc. 1961 Symp. Intern. Ecuac. Diff. Ordin., Mexico, pp. 158-163, 1962.
15. R. K. Miller and A. N. Michel, Ordinary Differential Equations, Academic Press: New York, 1982.
16. E. D. Sontag, Mathematical Control Theory, Springer-Verlag: New York, 1990.
17. M. Vidyasagar, Nonlinear Systems, 2nd edition, Prentice-Hall: Englewood Cliffs, NJ, 1993.
18. W. Walter, Differential and Integral Inequalities, Springer-Verlag: Berlin, 1970.