Enlargement of Contractive Sets of Discrete-Time Systems: The Generators Approach

In this paper, the problem of enlargement of positively invariant or contractive sets of discrete-time dynamical systems is investigated. In contrast to the usual approach consisting in describing regions of system'state space by their border surfaces, the dual description of sets in terms of a generator matrix and a, generally nonlinear, generator function is adopted. It is shown that this description allows the development of methods for the enlargement of positively invariant or contractive sets by simply adding a new generator in their generator matrix and then by establishing invariance or contractivity properties of an augmented system. As an application of this general result established for nonlinear systems, an approach of enlarging positively invariant or contractive sets for affine systems is presented.