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We present two theoretical results on the computation of &#x03BB;-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 &#x03BB;-contractive set with a given precision using 1-step sets. Second, based on the former result, we provide a procedure for choosing &#x03BB; so that the associated maximal &#x03BB;-contractive set is guaranteed to approximate the maximal controlled invariant set with a given accuracy.

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