Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the Kreĭn-Rutman theorem and its applications to controllability

Authors: Vũ Ngọc Phát and Trinh Cong Dieu
Journal: Proc. Amer. Math. Soc. 120 (1994), 495-500
MSC: Primary 47N70; Secondary 47H04, 93B05
MathSciNet review: 1182706
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper extends Krein-Rutman's theorem on linear operators leaving an invariant cone in infinite-dimensional Banach spaces to multivalued convex functions. The result is applied to obtain necessary and sufficient conditions for global controllability and reachability of nonlinear discrete-time systems described by convex processes.

References [Enhancements On Off] (What's this?)

  • [1] Jean-Pierre Aubin and Ivar Ekeland, Applied nonlinear analysis, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1984. A Wiley-Interscience Publication. MR 749753
  • [2] Jean-Pierre Aubin, Halina Frankowska, and Czesław Olech, Controllability of convex processes, SIAM J. Control Optim. 24 (1986), no. 6, 1192–1211. MR 861094,
  • [3] Ruth F. Curtain and Anthony J. Pritchard, Infinite dimensional linear systems theory, Lecture Notes in Control and Information Sciences, vol. 8, Springer-Verlag, Berlin-New York, 1978. MR 516812
  • [4] M. G. Krein and M. A. Rutman, Linear operator leaving invariant a cone in Banach spaces, Uspekhi Mat. Nauk 10 (1962), 199-325.
  • [5] V. I. Korobov and Nguen Hoa Son, Controllability of linear systems in a Banach space in the presence of constraints on the control. II, Differentsial′nye Uravneniya 16 (1980), no. 6, 1010–1022, 1146–1147 (Russian). MR 579679
  • [6] Nguyá»…n Khoa So’n, Controllability of linear discrete-time systems with constrained controls in Banach spaces, Control Cybernet. 10 (1981), no. 1-2, 5–17 (1982) (English, with Russian and Polish summaries). MR 686014
  • [7] Vu Ngoc Phat, Controllability of discrete-time dynamical systems, Ph.D. thesis, Azerbaidzan Univ., Bacu, USSR, 1984. (Russian)
  • [8] -, Controllability of linear systems with multiple delays on controls and states in Banach spaces, Internat. J. Control 5 (1989), 1645-1654.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47N70, 47H04, 93B05

Retrieve articles in all journals with MSC: 47N70, 47H04, 93B05

Additional Information

Article copyright: © Copyright 1994 American Mathematical Society