Abstract
In this paper, local stabilization for semi-linear abstract difference systems is considered. Specifically, we study the semi-linear difference system , , where are bounded linear operators acting on a Banach space X, are X-valued bounded linear operators defined on a Banach space U and f is a given nonlinear function. Assuming appropriate conditions, we will show that the local stabilization of the ‘frozen’ (time invariant) system for each fixed integer m, implies the local stabilization of the time varying semi-linear system. For such systems, explicit conditions for the local feedback exponential stabilizability are established. As an application of the main results, we study the local exponential stabilizability of a general abstract nonlinear control system.
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