A constructive approach to linear lyapunov functions for positive switched systems using collatz-wielandt sets

IEEE Transactions on Automatic Control

Volumn 58, Issue 3, 2013, Pages 748-751

  Doan, Thai Son ^a,b   Kalauch, Anke ^c   Siegmund, Stefan ^c  

^a INSTITUTE OF MATHEMATICS   (Viet Nam)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

^c DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Collatz Wielandt set; linear Lyapunov function; positive switched system

Indexed keywords

COLLATZ-WIELANDT SET; CONSTRUCTIVE APPROACH; SWITCHED SYSTEM;

SWITCHING SYSTEMS;

LYAPUNOV FUNCTIONS;

EID: 84874595950     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2012.2209270     Document Type: Article

References (7)

1. G. P. Barker and H. Schneider, "Algebraic Perron-Frobenius theory," Linear Algebra Appl., vol. 11, no. 3, pp. 219-233, 1975.
2. I. Bondarenko, "Dynamics of piecewise linear maps and sets of nonnegative matrices," Linear Algebra Appl., vol. 431, no. 5-7, pp. 495-510, 2009.
3. E. Fornasini and M. E. Valcher, "Linear copositive functions for continuous-time positive switched systems," IEEE Trans. Autom. Control, vol. 55, no. 8, pp. 1933-1937, Aug. 2010.
4. S. Gaubert and J. Gunawardena, "The Perron-Frobenius theorem for homogeneous, monotone functions," Trans. Amer. Math. Soc., vol. 356, no. 12, pp. 4931-4950, 2004. (Pubitemid 39603829)
5. F. Knorn, O. Mason, and R. Shorten, "On linear co-positive Lyapunov functions for sets of linear positive systems," Automatica, vol. 45, pp. 1943-1947, 2009.
6. H. Minc, Nonnegative Matrices. New York: Wiley, 1988.
7. W. H.M. Zijm, "Generalized eigenvectors and sets of nonnegative matrices," Linear Algebra Appl., vol. 59, pp. 91-113, 1984.