The stability robustness of generalized eigenvalues

Abstract

The concept of stability radius is generalized to matrix pairs. A matrix pair is said to be stable if its generalized eigenvalues are located in the open left half of the complex plane. The stability radius of a matrix pair (A, B) is defined to be the norm of the smallest perturbation Delta A such that (A+ Delta A, B) is unstable. The purpose is to estimate the stability radius of a given matrix pair. Depending on whether the matrices under consideration are complex or real, the problem can be classified into two cases. The complex case is easy and a complete solution is provided. The real case is more difficult, and only a partial solution is given.