In this paper, applying the method of nonlinear perturbation analysis [8, 9], we derive new nonlocal perturbation bounds for the problem considered which are less conservative than those in [1].

This disadvantage may be overcome using the methods of nonlinear perturbation analysis [7, 12].

Consider first the nonlocal perturbation analysis of the Riccati equation (2.

PETKOV,, Perturbation analysis of linear control problems, in Proceedings of the 10th IFAC World Congress, Munich, 1987, vol.

CHRISTOV, Perturbation analysis of the continuous and discrete matrix Riccati equations, in Proceedings of the 1986 American Control Confererence, Seattle, vol.

7] --, Nonlocal perturbation analysis of the Schur system of a , SIAM J.

While the perturbation analysis for classical and generalized eigenvalue problems is well studied (see [20, 33, 38]), for polynomial eigenvalue problems the situation is much less satisfactory and most research is very recent; see [22, 23, 24, 35, 36].

While the perturbation analysis and the construction of backward errors for finite eigenvalues have been studied in detail, there are only few results associated with the eigenvalue infinity.

When the degree is m = 1, we present the perturbation analysis for the case of T-even and T-odd matrix pencils and we show that the nearest perturbed pair can have 0 and [infinity] as eigenvalues depending on the choice of ([lambda], [mu]) for which we want to compute the backward error.

In this paper we have extended these results in the homogeneous setup of matrix polynomials which is a more convenient way to do the general perturbation analysis for matrix polynomials in that it equally treats all eigenvalues of a regular matrix polynomial.

AHMAD, Pseudospectra of matrix pencils and their applications in the perturbation analysis of eigenvalues and eigendecompositions, PhD Thesis, Dept.