Let be a non-empty, bounded, linearly ordered set and , for . A vector is said to be a -eigenvector of a square matrix if for some . A given matrix is called (strongly) -robust if for every the vector is a (greatest) eigenvector of for some natural number . We present a characterization of -robust and strongly -robust matrices. Building on this, an efficient algorithm for checking the -robustness and strong -robustness of a given matrix is introduced.