Set stabilization of sampled-data nonlinear differential inclusions via their approximate discrete-time models

Abstract

We present conditions under which a family of controllers that semiglobally-practically asymptotically (SPA) stabilizes a set for a family of discrete-time approximations of a nonlinear differential inclusion also SPA stabilizes that set for the inclusion's family of exact discrete-time models, for sufficiently small sampling periods. The result has the following important features: it does not require any regularity assumptions on the designed controllers; it is applicable to dynamic control laws; and it is stated for stability with respect to sets that are not necessarily compact.