This paper presents new necessary and sufficient linear programming conditions for convex closed polyhedra to be /spl lambda/-contractive with respect to discrete-time linear systems with saturating feedback control inputs. Based on linear programming formulation of these conditions, an effective procedure is proposed for construction of /spl lambda/-contractive polyhedra with nonempty intersection with the region of nonlinear behavior of the closed-loop system. The procedure starts with the supremal /spl lambda/-contractive polyhedron contained in the region of linear behavior and progressively expands it over the region of nonlinear behavior.
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