THE STABILITY ROBUSTNESS OF GENERALIZED EIGENVALUES

This note generalizes the concept of stability radius 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. Our 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 aa complete solution is provided. The real case is more difficult and only a partial solution is given.