In this paper, the robust a-stability problem of matrix second-order systems with perturbations in the form of a one-parameter family of matrices is investigated. All the system matrices, including the second-order differential coefficient matrices, are assumed to have such perturbations. Based on the Kronecker product, a necessary and sufficient condition for the robust a-stability problem is presented by transforming such a problem into checking the nonsingularity of a class of uncertain matrices. Then, a closed form for the maximal perturbation bounds for preserving the a-stability is given. Finally, illustrative examples are given to show that our results are effective and less conservative than the results obtained by other researchers. (C) 2012 Elsevier Ltd. All rights reserved.