Further comments on "vector norms as Lyapunov functions for linear systems"

IEEE Transactions on Automatic Control

Volumn 43, Issue 2, 1998, Pages 289-291

  Loskot, K ^a   Polanski A ^b   Rudnicki, R ^c  

^a UNIVERSITY OF SILESIA   (Poland)

^b SILESIAN UNIVERSITY OF TECHNOLOGY   (Poland)

^c INSTITUTE OF MATHEMATICS   (Poland)

Author keywords

Extensions of linear operators; Lyapunov functions; Stability

Indexed keywords

EID: 0010969679     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.661083     Document Type: Review

References (13)

1. G. Bitsoris, "Positively invariant polyhedral sets of discrete-time linear systems," Int. J. Contr., vol. 47, no. 6, pp. 1713-1726, 1988.
2. E. Deutsch, "On matrix norms and logarithmic norms," Numer. Math., vol. 24, pp. 49-51, 1975.
3. V. A. Desoer and H. Haneda, "The measure of a matrix as a tool to analyze computer algorithms for circuit analysis," IEEE Trans. Circuit Theory, vol. CT-19, pp. 480-486, 1972.
4. N. Dunford and J. T. Schwartz, Linear Operators, Part I, General Theory. New York: Intersci., 1967.
5. A. Hmamed, "Comments on 'Vector norms as Lyapunov functions for linear systems,'" IEEE Trans. Automat. Contr., vol. 39, p. 2522, Dec. 1994.
6. L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces. Moscow: Fizmatgiz, 1959 (in Russian).
7. H. Kiendl, J. Adamy, and P. Stelzner, "Vector norms as Lyapunov functions for linear systems," IEEE Trans. Automat. Contr., vol. 37, pp. 839-842, June 1992.
8. A. P. Molchanov and E. S. Pyatnitskiy, "Lyapunov functions that specify necessary and sufficient conditions of absolute stability of nonlinear nonstationary control systems III," Automat. Remote Contr., vol. 47, pp. 620-630, 1986.
9. A. P. Molchanov, "Lyapunov functions for nonlinear discrete-time control systems," Automat. Remote Contr., vol. 48, pp. 26-35, 1987.
10. K. Petersen, Ergodic Theory. U.K.: Cambridge Univ., 1983.
11. H. H. Rosenbrock, "A Lyapunov function with applications to some nonlinear physical systems," Automatica, vol. 1, pp. 31-53, 1963.
12. M. Vassilaki and G. Bitsoris, "Constrained regulation of linear continuous-time dynamical systems," Syst. Contr. Lett., vol. 13, pp. 247-252, 1989.
13. S. Weisenberger, "Piecewise-quadratic and piecewise-linear Lyapunov functions for discontinuous systems," Int. J. Contr., vol. 10, no. 2, pp. 171-180, 1969.