Duality results for the joint spectral radius and transient behavior

Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

Volumn 2005, Issue , 2005, Pages 2344-2349

  Plischke, Elmar ^a   Wirth, Fabian ^b   Barabanov, Nikita ^c  

^a UNIVERSITY OF BREMEN   (Germany)

^b NATIONAL UNIVERSITY OF IRELAND   (Ireland)

^c NORTH DAKOTA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; LINEAR ALGEBRA; THEOREM PROVING;

GROWTH RATE; LINEAR INCLUSIONS; SEMIGROUPS; TRANSIENT NORMS;

SYSTEMS ANALYSIS;

EID: 33847210344     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2005.1582512     Document Type: Conference Paper

References (19)

1. G.-C. Rota and G. Strang, "A note on the joint spectral radius," Indag. Math., vol. 22, pp. 379-381, 1960.
2. N. E. Barabanov, "Absolute characteristic exponent of a class of linear nonstationary systems of differential equations," Siberian Mathematical Journal, vol. 29, no. 4, pp. 521-530, 1988.
3. F. Colonius and W. Kliemann, "Maximal and minimal Lyapunov exponents of bilinear control systems," J. Diff. Eqns., vol. 101, pp. 232-275, 1993.
4. N. E. Barabanov, "Lyapunov indicator of discrete inclusions. I-III," Autom. Remote Control, vol. 49, no. 2, pp. 152-157, no. 3, pp. 283-287, no.5, pp. 558-565, 1988.
5. V. S. Kozyakin, "Algebraic unsolvability of problem of absolute stability of desynchronized systems," Autom. Rem. Control, vol. 51, no. 6, pp. 754-759, 1990.
6. F. Wirth, "The generalized spectral radius and extremal norms," Lin. Alg. Appl., vol. 342, pp. 17-40, 2002.
7. _, Stability theory of perturbed systems: Joint spectral radii and stability radii, ser. Lecture Notes in Mathematics. Berlin: Springer-Verlag, 2005, to appear.
8. G. Dahlquist, "Stability and error bounds in the numerical integration of ordinary differential equations," Tekn. Högskol. Handl., vol. 130, 1959.
9. S. M. Lozinskiǐ, "Error estimates for numerical integration of ordinary differential equations," Izv. Vysš. Učebn. Zaved Matematika, vol. 5, pp. 52-90, 1958, errata 5:222, 1959.
10. M. I. Gil', Stability of Finite and Infinite Dimensional Systems. Boston/Dordrecht/London: Kluwer Academic Publishers, 1998.
11. D. Hinrichsen and A. J. Pritchard, Mathematical Systems Theory I. Berlin: Springer-Verlag, 2005.
12. V. Y. Protasov, "The joint spectral radius and invariant sets of linear operators," Fundam. Prikl. Mat., vol. 2, no. 1, pp. 205-231, 1996.
13. W. Feller, "On the generation of unbounded semi-groups of bounded linear operators," Am. of Math., Ser. 2, vol. 58, pp. 166-174, 1953.
14. M. A. Berger and Y. Wang, "Bounded semigroups of matrices," Lin. Alg. Appl., vol. 166, pp. 21-27, 1992.
15. T. Ström, "On logarithmic norms," SIAM J. Numer. Anal., vol. 12, no. 5, pp. 741-753, 1975.
16. M. Vidyasagar, Nonlinear Systems Analysis, 2nd ed. Englewood Cliffs, NJ: Prentice Hall, 1993.
17. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge University Press, 1990.
18. R. T. Rockafellar, Convex Analysis. Princeton University Press, 1970.
19. F. H. Clarke, Y. S. Ledyaev, R. J. Stern, and P. R. Wolenski, Nonsmooth Analysis and Control Theory, New York: Springer, 1998, vol. 178.