In this paper, it is shown that for a fixed m ∈ N, Z/m is a stable set of sampling for V(φ 1 , φ 2 , . . . , φ s ) if and only if there exists γ > 0 such that | detΦ(x)| ≥ γ a.e. on T, where Φ is a symbol matrix of a block Laurent operator associated with the sample set of φ l , l = 1, . . . , s. A similar result is proved when rZ where r = p/q, p, q ∈ N and gcd(p, q) = 1,is a stable set of sampling for V(φ) (single generator) as well as V(φ 1 , φ 2 , . . . , φ s ) (multi generators). A perturbation of stable set of sampling is also discussed. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.