Maximal perturbation bounds for robust -stability of matrix second-order systems with one-parameter perturbations

In this paper, the robust α -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 α -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 α -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.