Shreemayee Bora

Perturbation theory for Hamiltonian matrices and the distance to bounded-realness

Motivated by the analysis of passive control systems, we undertake a detailed perturbation analysis of Hamiltonian matrices that have eigenvalues on the imaginary axis. We construct minimal Hamiltonian perturbations that move and coalesce eigenvalues of opposite sign characteristic to form multiple eigenvalues with mixed sign characteristics, which are then moved from the imaginary axis to specific locations in the complex plane by small Hamiltonian perturbations. We also present a numerical method to compute upper bounds for the minimal perturbations that move all eigenvalues of a given Hamiltonian matrix outside a vertical strip along the imaginary axis.

Linear Perturbation Theory for Structured Matrix Pencils Arising in Control Theory

We investigate the effect of linear perturbations on several structured matrix pencils arising in control theory. These include skew-symmetric/symmetric pencils arising in the computation of optimal H infty control and linear-quadratic control for continuous and discrete time systems.

Structured Eigenvalue Condition Number and Backward Error of a Class of Polynomial Eigenvalue Problems

Necessary and sufficient conditions are obtained for simple eigenvalues of complex matrix polynomials with

Structured Eigenvalue Backward Errors of Matrix Pencils and Polynomials with Hermitian and Related Structures

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Stability of eigenvalues and spectral decompositions under linear perturbation

-even/odd and

Effect of linear perturbation on spectra of matrices

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Structured eigenvalue backward errors of matrix pencils and polynomials with palindromic structures

-palindromic/antipalindromic structures to have the same normwise condition number with respect to structure preserving and arbitrary perturbations. Here,

Structured Eigenvalue Perturbation Theory

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Distance Problems for Hermitian Matrix Pencils with Eigenvalues of Definite Type

denotes either the transpose

Structured eigenvalue backward errors of matrix polynomials

T