Necessary and sufficient conditions for invariance of convex sets for discrete-time saturated systems

A convex analysis-based characterization of invariance and contractivity of compact convex sets for discretetime saturated systems is presented. Necessary and sufficient conditions for the existence of convex set-induced Lyapunov functions is provided. The results generalize the quadratic Lyapunov theory for saturated systems, apply also to asymmetric saturations and can be extended to affine nonlinearity maps. A numerical example illustrates the improvements of our method with respect to other classical ones.