A parameter-dependent Lyapunov function for a polytope of matrices

IEEE Transactions on Automatic Control

Volumn 45, Issue 8, 2000, Pages 1516-1519

  Mori, T ^a   Kokame, H ^b  

^a KYOTO INSTITUTE OF TECHNOLOGY   (Japan)

^b Osaka Prefecture University   (Japan)

Author keywords

Hurwitz stability; Parameter dependent Lyapunov function; Polytope of matrices; Quadratic stability

Indexed keywords

CONSTRAINT THEORY; FUNCTIONS; LYAPUNOV METHODS; PARAMETER ESTIMATION; POLYNOMIALS; SYSTEM STABILITY;

HURWITZ-STABILITY; QUADRATIC STABILITY;

CONTROL SYSTEM ANALYSIS;

EID: 0034247354     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.871762     Document Type: Article

References (10)

1. S. P. Bhattacharyya, H. Chapellat, and L. H. Keel, Robust Control. Upper Saddle River, NJ: Prentice-Hall, 1995.
2. B. R. Barmish, New Tools for Robustness of Linear Systems. New York: MacMillan, 1994.
3. B. R. Barmish and H. I. Kang, "A survey of extreme point results for robustness of control systems," Automatica, vol. 29, no. 1, pp. 13-35, 1993.
4. S. Barnett and C. Storey, Matrix Methods in Stability Theory. London, U.K.: Nelson, 1970.
5. T. Mori and H. Kokame, "On quadratic Hurwitz stability of interval polynomials," Trans. SICE, vol. 34, pp. 450-455, 1998.
6. Y. Mori, T. Mori, and Y. Kuroe, "A solution to the common Lyapunov function problem for continuous-time systems," in Proc. 1997 Conf. Decision and Control, San Diego, CA, pp. 3530-3531.
7. G. Chockalingam, S. Dasgupta, B. D. O. Anderson, and M. Fu, "Lyapunov functions for uncertain systems with applications to the stability of time varying systems," in Proc. 1993 Conf. Decision and Control, San Antonio, TX, pp. 1525-1530.
8. P. Gahinet, P. Apkarian, and M. Chilai, "Affine parameter-dependent Lyapunov functions and real parameter uncertainty," IEEE Trans. Automat. Contr., vol. 41, pp. 436-442, Mar. 1996.
9. F. Amato, M. Corless, M. Mattei, and R. Setola, "A multivariable stability margin in the presence of time-varying bounded rate gains," Int. J. Robust and Nonlinear Contr., vol. 7, pp. 127-143, 1997.
10. M. Corless, "Robust stability analysis and controller design with quadratic Lyapunov functions," in Variable Structure and Lyapunov Control, A. S. I. Zinober, Ed. London, U.K.: Springer, 1994.