Nonquadratic Lyapunov Functions for Robust Stability Analysis of Linear Uncertain Systems

IEEE Transactions on Automatic Control

Volumn 39, Issue 1, 1994, Pages 135-138

  Zelentsovsky, A L ^a  

^a Redwood Hwy ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL NONLINEARITIES; CONTROL SYSTEM ANALYSIS; LYAPUNOV METHODS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; NONLINEAR PROGRAMMING; PARAMETER ESTIMATION; ROBUSTNESS (CONTROL SYSTEMS); STATE ESTIMATION; SYSTEM STABILITY; VECTORS;

GLOBAL ASYMPTOTIC STABILITY; UNCERTAINTY BOUNDS;

LINEAR CONTROL SYSTEMS;

EID: 0028282375     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/9.273350     Document Type: Article

References (12)

1. D. S. Bernstein and W. M. Haddad, “Robust stability and performance analysis for linear dynamic systems,” IEEE Trans. Automat. Contr., vol. 34, pp. 751–758, July 1989.
2. A. R. Galimidi and B. R. Barmish, “The constrained Lyapunov problem and its application to robust output feedback stabilization,” IEEE Trans. Automat. Contr., vol. 31 pp. 410–419, May 1986.
3. L. H. Keel, S. P. Bhattacharyya, and J. W. Howze, “Robust control with structured perturbations,” IEEE Trans. Automat. Contr., vol. 33, pp. 68–78, Jan. 1988.
4. M. A. Led l and J. S. Gibson, “A first order Lyapunov robustness method for linear systems with uncertain parameters,” IEEE Trans. Automat. Contr., vol. 35, pp. 1068–1070, Sept. 1990.
5. R. K. Yedavalli and Z. Liang. “Reduced conservatism in stability robustness bounds by state transformation, IEEE Trans. Automat. Contr., vo l. 31, pp. 863–866, Sept. 1986.
6. K. Zhou and P. P. Ithargonekar, “Stability robustness bounds for linear state-space models with structured uncertainty,” IEEE Trans. Automat. Contr., vol. 32, pp. 621–623, July 1987.
7. R. W. Brockett, “Lie algebras and Lie groups in control theory,” in Geometric Methods in System Theory. D. Q. Mayne and R. W. Brockett, Eds. Dordrecht: Reidel, pp. 213–225, 1973.
8. J. Baillieul, “The geometry of homogeneous polynomial dynamical systems,” Nonlinear Analysis, Theory, Methods Appl., vol. 4, no. 5, pp. 879–900, 1980.
9. A. I. Barlcin and A. L. Zelentsovsky, “Method of power transformations for analysis of stability of nonlinear control systems,” Syst. Contr. Letts., vol. 3, pp. 303–310, 1983.
10. E. S. Piatnitskiy and V. I. Skorodinskiy, “Numerical methods of Lyapunov functions construction and their application to the absolute stability problem,” Systems Contr. Letts., vol. 2, pp. 130–135, 1982.
11. A. H. Gelig, G. A. Leonov, and V. A. Yakubovich, Stability of Systems with Multiple Equilibria. Moscow: Nauka 1978 (in Russian).
12. P. Lancaster, Theory of Matrices. New York: Academic Press, 1969.