On the computation of lambda-contractive sets for linear constrained systems

摘要

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