The generalized eigenstructure problem in linear system theory

The algebraic theory of linear time-invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context. In this paper the numerical aspects of a certain class of such algorithms-dealing with what the author calls generalized eigenstructure problems-are discussed. Some new and/or modified algorithms are presented. Both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria.