A conjecture on the existence of common quadratic Lyapunov functions for positive linear systems

Proceedings of the American Control Conference

Volumn 5, Issue , 2003, Pages 4469-4470

  Mason, Oliver ^a   Shorten, Robert ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; LYAPUNOV METHODS; MATRIX ALGEBRA; SYSTEM STABILITY; THEOREM PROVING;

LINEAR TIME-INVARIANT (LTI) SYSTEMS;

LINEAR CONTROL SYSTEMS;

EID: 0142199976     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (9)

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2. R. N. Shorten and K. Narendra, "Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a finite number of stable second order linear time-invariant systems," International Journal of Adaptive Control and Signal Processing, In Press.
3. R. Shorten, F. Ó Cairbre, and P. Curran, "On the dynamic instability of a class of switching systems," in Proceedings of IFAC conference on Artificial Intelligence in Real Time Control, 2000.
4. L. Farina and S. Rinaldi, Positive linear systems. Wiley Interscience Series, 2000.
5. R. Horn and C. Johnson, Topics in matrix analysis. Cambridge University Press, 1991.
6. D. Stipanovic and D. Siljak, "Stability of polytopic systems via convex M-matrices and parameter-dependent Lyapunov functions," Nonlinear Analysis, vol. 40, pp. 589-609, 2000.
7. O. Mason and R. Shorten, "A conjecture on the existence of common quadratic Lyapunov functions for positive linear systems," tech. rep., NUIM SS/2002/09, 2002.
8. Y. Mori, T. Mori, and Y. Kuroe, "On a class of linear constant systems which have a common quadratic Lyapunov function," in Proceedings of 37th Conference on Decision and Control, 1998.
9. K. Narendra and J. Balakrishnan, "A Common Lyapunov Function for Stable LTI Systems with Commuting A-Matrices," IEEE Transactions on Automatic Control, vol. 39, no. 12, pp. 2469-2471, 1994.