Robust set invariance and contractivity of discrete-time systems: The generators approach

In this paper, the problem of robust set invariance and contractivity with respect to discrete-time dynamical systems is investigated. In contrast to the usual approach consisting in describing regions of system´s space by their border surfaces, a dual description of sets in terms of a generator matrix and a, generally nonlinear, generating function is proposed. This leads to the establishment of an associated generated system whose robust set invariance and/or contractivity properties imply corresponding properties for the initial system. This general result is then applied to the development of robust set invariance and/or robust contractivity conditions for linear systems.