Spectral abscissa

In mathematics, the spectral abscissa of a matrix or a bounded linear operator is the greatest real part of the matrix's spectrum (its set of eigenvalues)., the spectral abscissa maps a square matrix onto its largest real eigenvalue.[2] Let λ1, ..., λs be the (real or complex) eigenvalues of a matrix A ∈ Cn × n. Then its spectral abscissa is defined as: In stability theory, a continuous system represented by matrixis said to be stable if all real parts of its eigenvalues are negative, i.e.[3] Analogously, in control theory, the solution to the differential equation

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