Lyapunov Functions for Diagonally Dominant Systems

This paper deals with the construction of Lyapunov functions for the finite dimensional linear system ẋ = Ax when the entries of the generating matrix A satisfy various conditions requiring dominance of its diagonal elements and nonnegativity of its off-diagonal elements. The particular case in which the system defines a Markov chain is given special attention and it is shown that the results then imply certain inequalities which have an intuitively appealing information theoretic significance.