Stability Criteria and Localization of the Matrix Spectrum in Terms of Trace Functions

New necessary and sufficient conditions for the asymptotic stability and localization of the spectra of linear autonomous systems are proposed by using the matrix trace functions. The application of these conditions is reduced to the solution of two scalar inequalities for a symmetric positive-definite matrix. As a corollary, for linear control systems, we present a procedure aimed at the construction of the set of stabilizing measurable output feedbacks.