Interval Matrix Systems and Invariance of Non-Symmetrical Contractive Sets

The paper studies the set invariance properties exhibited by the linear dynamics of interval matrix systems (abbreviated IMSs). The considered sets have non-symmetrical shapes defined by arbitrary Holder p-norms and are exponentially contractive (with exponential time-decrease). For such sets we provide two types of results that allow invariance tests: (i) sufficient conditions for 1 <= p <= 1, (i i) necessary and sufficient conditions for p is an element of{1, infinity}. Our approach includes, in generalized forms, results previously reported by other works referring to either non-symmetrical sets invariant with respect to single-model systems, or symmetrical sets invariant with respect to IMSs. Our presentation focuses on continuous-time IMSs, whereas the discrete-time case is briefly addressed by the key elements of a basic analogy. An example already used in the IMS literature illustrates the applicability of our theoretical developments.