Hurwitz matrix

A square matrixMathworldPlanetmath A is called a Hurwitz matrix if all eigenvaluesMathworldPlanetmathPlanetmathPlanetmathPlanetmath of A have strictly negative real part, Re[λi]<0; A is also called a stability matrix, because the feedback system


is stable.

If G(s) is a (matrix-valued) transfer function, then G is called Hurwitz if the poles of all elements of G have negative real part. Note that it is not necessary that G(s), for a specific argument s, be a Hurwitz matrix — it need not even be square. The connection is that if A is a Hurwitz matrix, then the dynamical systemMathworldPlanetmathPlanetmath

x˙(t) = Ax(t)+Bu(t)
y(t) = Cx(t)+Du(t)

has a Hurwitz transfer function.

Reference: Hassan K. Khalil, Nonlinear Systems, Prentice Hall, 2002

Title Hurwitz matrix
Canonical name HurwitzMatrix
Date of creation 2013-03-22 14:02:45
Last modified on 2013-03-22 14:02:45
Owner lha (3057)
Last modified by lha (3057)
Numerical id 4
Author lha (3057)
Entry type Definition
Classification msc 93D99
Defines Hurwitz transfer function
Defines stability matrix