Robust set invariance and contractivity of continuous-time systems

In this paper, the problem of set invariance and contractivity with respect to continuous-time dynamical systems is investigated. In contrast to the usual approach consisting in describing regions of system´s state space by their border surfaces, a dual description of sets in terms of a generator matrix and a, generally nonlinear, generator function is proposed. This leads to the establishment of an associated generated system whose 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 contractivity conditions for linear and nonlinear systems.