Structured Backward Errors for Eigenvalues of Linear Port-Hamiltonian Descriptor Systems

When computing the eigenstructure of matrix pencils associated with passivity analysis perturbed port-Hamiltonian descriptor system using a structured generalized eigenvalue method, one should make sure that computed spectrum satisfies symmetries corresponds to this structure and underlying physical system. We perform backward error show for systems given correct symmetry there always exists nearby exactly eigenstructure. also derive bounds how near is stability radius plays role in bound.