Perturbations of Solution Sets of Linear Systems

Abstract

This chapter is devoted to the analysis of stability and perturbations of the feasible criterion set (FCS). This problem is extremely important since the data are usually disturbed to a certain extent in real-life applications. It is required that the resulting perturbations of an FCS are not too substantial. In other words, an FCS must depend on the data disturbances in a continuous way. This chapter deals with the estimation of such perturbations in the linear case. The problem is reduced to estimating perturbations of the feasible decision set given by a system of linear inequalities and equalities. To be precise, the distance between two sets, the original set and the perturbed set is estimated.