Obtaining stabilizing stationary controls via finite horizon cost

This paper focuses on the stabilizing properties of stationary feedback controls for general nonlinear systems that are obtained by minimizing a finite horizon cost, in a receding horizon control basis. The main result is to establish exponential stability for stationary controls obtained from minimization of sufficiently large but finite time horizon cost. The approach requires a previously defined notion of closed-loop detectability of nonlinear systems, and in the present paper we introduce conditions under which the aforementioned detectability sense is verified from the open-loop system data, as is usual in linear systems. In connection, we verify that stabilizable and detectable linear time-invariant systems satisfy each of the work assumptions