Let E be a Banach space over C and let the densely defined closed linear operator A: D(A) ... EQ E be discretely approximated by the sequence ((An, D(An)))n ¥N of operators An where each An is densely defined in the Banach space Fn. Let sa(A) be the approximate point spectrum of A and let se(An) denote the e-pseudospectrum of An. Generalizing our own result, we show that sa(A) ... lim inf se(An...

Pseudospectra provide an analytical and graphical alternative for investigating nonnormal matrices and operators, give a quantitative estimate of departure from non-normality and give information about stability. In this paper, we prove that pseudospectral radius is sub-additive and sub-multiplicative for a commuting pair of matrices over the complex field, extending the same result for spectra...

In this work, we introduce and study the S-pseudospectra of linear operators defined by nonstrict inequality in a Hilbert space. Inspired A. B?ttcher?s result [3], prove that S-resolvent norm bounded is not constant any open set set. Beside, find characterization S-pseudospectrum operator means S-spectra all perturbed with perturbations have norms strictly less than ?.

This lecture is mainly inspired by a paper of Y. Almog appearing last year at Siam J. Math. Anal. Our goal here is first to discuss in detail the simplest models which we think are enlightning for understanding the role of the pseudospectra in this question and secondly to present proofs which will have some general character and will for example apply in a more physical model, for which we hav...

The pseudospectrum has become an important quantity for analyzing stability of nonnormal systems. In this paper, we prove a mapping theorem for pseudospectra, extending an earlier result of Trefethen. Our result consists of two relations that are sharp and contains the spectral mapping theorem as a special case. Necessary and sufficient conditions for these relations to collapse to an equality ...

We describe how to obtain bounds on the spectrum of a non-self-adjoint operator by means of what we call its higher order numerical ranges. We prove some of their basic properties and describe explain how to compute them. We finally use them to obtain new spectral insights into the non-selfadjoint Anderson model in one and two space dimensions. keywords: non-self-adjoint operator, spectrum, num...

This letter assesses the impact of cyber-attacks on control system modular multilevel converter (MMC)-based high-voltage dc (MMC-HVdc) transmission technology. Specifically, small-signal model MMC-HVdc is characterized by a closed-loop matrix and distance to instability then quantified structured pseudospectrum. Furthermore, vertical search method proposed quantify boundary The quantification w...

In this paper we discuss the problem of computing the H∞-norms of transfer functions associated to large-scale descriptor systems. We exploit the relationship between the H∞-norm and the structured complex stability radius of the corresponding system pencil. To compute the structured stability radius we consider so-called structured pseudospectra. Namely, we have to find the pseudospectrum that...

Let A be a matrix with distinct eigenvalues and let w(A) be the distance from A to the set of defective matrices (using either the 2norm or the Frobenius norm). Define Λ , the -pseudospectrum of A, to be the set of points in the complex plane which are eigenvalues of matrices A + E with ‖E‖ < , and let c(A) be the supremum of all with the property that Λ has n distinct components. Demmel and Wi...