On the Kreĭn-Rutman theorem and its applications to controllability

Phát, Vũ Ngọc; Dieu, Trinh Cong

doi:10.1090/S0002-9939-1994-1182706-X

On the Kreĭn-Rutman theorem and its applications to controllability
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by Vũ Ngọc Phát and Trinh Cong Dieu PDF

Proc. Amer. Math. Soc. 120 (1994), 495-500 Request permission

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.

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