Some authors also use the term stability matrix.
[2] Such matrices play an important role in control theory.
is called a Hurwitz matrix if every eigenvalue of
has strictly negative real part, that is, for each eigenvalue
Any hyperbolic fixed point (or equilibrium point) of a continuous dynamical system is locally asymptotically stable if and only if the Jacobian of the dynamical system is Hurwitz stable at the fixed point.
The Hurwitz stability matrix is a crucial part of control theory.
Similarly, a system is inherently unstable if any of the eigenvalues have positive real components, representing positive feedback.
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