On a common quadratic Lyapunov function for widely distant systems

IEEE Transactions on Automatic Control

Volumn 42, Issue 12, 1997, Pages 1697-1699

  Ooba, Tatsushi ^a   Funahashi, Yasuyuki ^a  

^a NAGOYA INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Linear dynamical systems; Lyapunov stability; Positive matrices

Indexed keywords

FUNCTIONS; LINEAR CONTROL SYSTEMS; LYAPUNOV METHODS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES; POLYNOMIALS; PROBLEM SOLVING; RICCATI EQUATIONS; THEOREM PROVING;

LINEAR DYNAMICAL SYSTEMS; LYAPUNOV INEQUALITIES; WIDELY DISTANT SYSTEMS;

SYSTEM STABILITY;

EID: 0031354389     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.650019     Document Type: Article

References (9)

1. M. Rotea and P. Khagonekar, "Stabilization of uncertain systems with norm bounded uncertainty - A control Lyapunov function approach," SIAM J. Contr. Optim., vol. 27, pp. 1462-1476, 1989.
2. K. S. Narendra and J. Balakrishnan, "A common Lyapunov function for stable LTI systems with commuting A-matrices," IEEE Trans. Automat. Contr., vol. 39, pp. 2469-2471, 1994.
3. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Studies in Applied Mathematics, vol. 15. Philadelphia, PA: SIAM, 1994.
4. T. Ooba and Y. Funahashi, "Two conditions concerning common quadratic Lyapunov function for noncommutative systems," IEEE Trans. Automat. Contr., vol. 42, pp. 719-721, 1997.
5. _, "Stability robustness for linear state space models - A Lyapunov mapping approach," Syst. Contr. Lett., vol. 29, pp. 191-196, 1997.
6. G. Hewer and C. Kenney, "The sensitivity of the stable Lyapunov equation," SIAM J. Contr. Optim., vol. 26, pp. 321-344, 1988.
7. K. Zhou and P. Khargonekar, "Stability robustness for linear state space models with structured uncertainty," IEEE Trans. Automat. Contr., vol. AC-32, pp. 621-623, 1987.
8. D. Gale and H. Nikaido, "The Jacobian matrix and global univalence mappings," Math. Ann., vol. 19, pp. 81-93, 1965.
9. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences. New York: Academic, 1979.