Algebraic criteria for a class of contractive symmetrical sets invariant with respect to arbitrary switching linear dynamics
Octavian C. Pastravanu, Mihaela-Hanako Matcovschi · 2020
The paper considers the discrete- or continuous-time dynamics of arbitrary switching linear systems, for which new results are developed on set invariance testing. The invariance analysis refers to a class of contractive sets, previously studied only for a few simple cases; our developments cover the general circumstances of polyhedral sets exhibiting full “orthant-symmetry”, i.e. symmetry with respect to each of the state-space axes. We provide algebraic criteria (stated in terms of matrix equalities, constrained by some matrix norm / measure inequalities), which are necessary and sufficient for the characterization of the considered contractive sets. Simplified forms of these results are derived as sufficient conditions. The paper also comments on the connections to other works and illustrates the applicability of the theoretical points for a numerical example.