Sensitivity analysis of linear systems—a structural approach

Abstract

An approach to the sensitivity analysis of systems modelled as a set of linear algebraic equations Ax = b is presented. First- and second-order sensitivities of the system variables to changes in system parameters, i.e. non-zero elements of the matrix A, are derived. Two kinds of parameter perturbation are discussed: single parameter perturbation and perturbations of all the system parameters. A structural approach is applied, consisting in partitioning of the system into a number of irreducible, acyclically interconnected subsystems. This approach reduces the computational effort and yields a qualitative sensitivity assessment; i.e. it is possible to exclude the influence of certain parameters on some variables.