On the Computation of $\lambda$- Contractive Sets for Linear Constrained Systems

Abstract

We present two theoretical results on the computation of $\lambda$ - contractive sets for linear systems with state and input constraints. First, we show that it is possible to a priori compute a number of iterations that is sufficient to approximate the maximal $\lambda$ - contractive set with a given precision using 1-step sets. Second, based on the former result, we provide a procedure for choosing $\lambda$ so that the associated maximal $\lambda$ - contractive set is guaranteed to approximate the maximal controlled invariant set with a given accuracy.