A Semi-Definite Lyapunov Theorem and the Characterization of Tridiagonal D-Stable Matrices
David H Carlson, Biswa Nath Datta, Charles R. Johnson · SIAM Journal on Algebraic and Discrete Methods · 1982
A new necessary and sufficient condition is given for an $n \times n$ complex matrix A to be stable. It involves a positive semi-definite image under a Lyapunov map and the real and imaginary parts of A. This condition is then used to characterize the real tridiagonal matrices which are D-stable, and those which are totally D-stable.