Spectral abscissa

In mathematics, the spectral abscissa of a matrix or a bounded linear operator is the supremum among the real part of the elements in its spectrum, sometimes denoted as formula_1
Matrices.
Let λ1, ..., λ"s" be the (real or complex) eigenvalues of a matrix "A" ∈ C"n" × "n". Then its spectral abscissa is defined as:
For example, if the set of eigenvalues were = {1+3i,2+3i,4-2i}, then the Spectral abscissa in this case would be 4.
It is often used as a measure of stability in control theory, where a continuous system is stable if all its eigenvalues are located in the left half plane, i.e. formula_3