Weak Asymptotic Stabilizability of Discrete-Time Systems Given by Set-Valued Operators*

The paper deals with the weak asymptotic stabilizability property of discrete-time inclusions, whose right-hand sides are set-valued operators in Banach spaces. Such inclusions include control systems with constrained controls. Questions of existence of positive eigenvalues of convex closed operators are discussed. Based on the method of decomposition of the state space we derive sufficient conditions for weakly asymptotic stabilizability of discrete-time convex processes in terms of controllability-like conditions. The results are applied in weak asymptotic stabilizability of linear discrete and continuous-time systems with constrained controls in Banach spaces.