The non-symmetrical case of invariant-set analysis with respect to linear dynamics

Abstract

The class of instruments available for set invariance analysis with respect to linear system dynamics is significantly wider for sets that are symmetrical (relative to the state-space origin), compared with the non-symmetrical case. Our work provides a new result for testing the invariance of non-symmetrical sets, described by general forms. For any considered set, the instantaneous shape is defined by the help of a Hőlder p-norm, 1 ≤ p ≤ ∞, applied to a smooth vector function, whose components are time-and region-dependent. We also show that our invariance testing procedure incorporates, as particular cases, some results already known, separately proved by different authors.