Robust stability of a class of nonlinear time-varying discrete systems

ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings

Volumn 3, Issue , 2001, Pages 557-560

  Liu, Derong ^a   Molchanov, Alexander ^a  

^a 1120 Science and Engineering Offices   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRAIC CRITERIA; LYAPUNOV SECOND METHOD; MATRIX EQUATIONS; NONLINEAR DISCRETE-TIME SYSTEMS; ROBUST ABSOLUTE STABILITY; SECTOR NONLINEARITY; SOLVABILITY CONDITIONS; VARIATIONAL METHODS;

DIGITAL CONTROL SYSTEMS; DISCRETE TIME CONTROL SYSTEMS; LYAPUNOV FUNCTIONS; MATRIX ALGEBRA; ALGEBRA; ALGORITHMS; LINEAR PROGRAMMING; LYAPUNOV METHODS; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY; TIME VARYING SYSTEMS;

SYSTEM STABILITY; NONLINEAR SYSTEMS;

NONLINEAR TIME-VARYING DISCRETE SYSTEMS; ROBUST STABILITY;

EID: 0035020683     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISCAS.2001.921371     Document Type: Conference Paper

References (20)

1. M. A. Aizerman and F. R. Gantmacher, Absolute Stability of Regulator Systems, San Francisco, CA: Holden-Day, 1964.
2. B. R. Barmish, New Tools for Robustness of Linear Systems, New York, NY: Macmillan, 1994.
3. P. H. Bauer, K. Premaratne, and J. Durán, "A necessary and sufficient condition for robust asỳmptotic stability of timevariant discrete systems", IEEE Transactions on Automatic Control, vol. 38, pp. 1427-1430, 1993.
4. S. P. Bhattacharyya, H. Chapellat, and L. H. Keel, Robust Control: The Parametric Approach, Upper Saddle River, NJ: Prentice-Hall, 1995.
5. L. T. Grujić and D. Petkovski, "On robustness of Lurie systems with multiple non-linearities", Automatica, vol. 23. pp. 327-334, 1987. (Pubitemid 17658207)
6. R. A. Horn and C. R. Johnson, Matrix Analysis, New York, NY: Cambridge University Press, 1985.
7. E. I. Jury, "Robustness of a discrete system", Automation and Remote Control, vol. 51, pp. 571-592, 1990.
8. E. J. Jury and B. W. Lee, "On the stability of a certain class of nonlinear sampled-data systems", IEEE Transactions on Automatic Control, vol. 9, pp. 51-61, 1964.
9. V. L. Kharitonov, "Asymptotic stability of an equilibrium position of a family of systems of linear differential equations", Differential Equations, vol. 14, pp. 1483-1485, 1979.
10. S. R. Kolla, R. K. Yedavalli, and J. B. Farison, "Robust stability bounds on time-varying perturbations for state-space models of linear discrete-time systems", International Journal of Control, vol. 50, pp. 151-159, 1989. (Pubitemid 20614277)
11. J. P. La Salle, The Stability and Control of Discrete Processes. New York, NY: Springer-Verlag, 1986.
12. A. P. Molchanov, "Conditions of uniform absolute stability of nonlinear nonstationary sampled-data systems", Automation and Remote Control, vol. 44, pp. 306-314, 1983. (Pubitemid 14466138)
13. A. P. Molchanov, "Lyapunov functions for nonlinear discretetime control systems", Automation and Remote Control, vol. 48, pp. 728-736, 1987.
14. K. S. Narendra and J. Balakrishnan, "A common Lyapunov function for stable LTI systems with commuting v4-matrices", IEEE Transactions on Automatic Control, vol. 39, pp. 2469-2471, 1994.
15. K. S. Narendra and J. H. Taylor, Frequency Domain Criteria for Absolute Stability, New York, NY: Academic Press, 1973.
16. A. Polański, "Lyapunov function construction by linear programming", IEEE Transactions on Automatic Control, vol. 42, pp. 1013-1016, 1997. (Pubitemid 127826263)
17. K. Premaratne and M. Mansour, "Robust stability of timevariant discrete-time systems with bounded parameter perturbations", IEEE Transactions on Circuits and Systems-It Fundamental Theory and Applications, vol. 42, pp. 40-45, 1995.
18. J. H. Su and I. K. Fong, "New robust stability bounds of linear discrete-time systems with time-varying uncertainties", International Journal of Control, vol. 58, pp. 1461-1467, 1993.
19. A. Tesi and A. Vicino, "Robust absolute stability of Lure control systems in parameter space", Automatica, vol. 27. pp. 147-151, 1991.
20. K. Wang, A. N. Michel, and D. Liu, "Necessary and sufficient conditions for the Hurwitz and Schur stability of interval matrices." IEEE Transactions on Automatic Control, vol. 39. pp. 1251-1255, June 1994.