A simple and fast algorithm for determining asymptotic stability of linear autonomous systems

The method introduced here determines explicitly whether a given system has only eigenvalues with negative real parts, without determining these eigenvalues, but rather by determining the eigenvalues of a related symmetric matrix which are always real and hence easy to calculate. The new method is similarly applied to linear autonomous discrete systems where all the eigenvalues of the system matrix are required to be positioned within the unit circle in the z-plane.