Brief paper: Lyapunov functions for diagonally dominant systems

Authors:
J. C. Willems
Affiliations:
Mathematical Institute, University of Groningen, P.O. Box 800, Groningen, The Netherlands
Venue:
Automatica (Journal of IFAC)
Year:
1976

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Abstract

Abstract: This paper deals with the construction of Lyapunov functions for the finite dimensional linear systemx@?= Ax when the entries of the generating matrixA 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.