This is for self-examination of the N-dimensional system of linear homogeneous ordinary differential equations of the form:
dx/dt=Ax
where A is the matrix of coefficients of the system.
I found out that you can check stability by determining if the real parts of all eigenvalues of A are negative. You can check for vibrations if there are purely imaginary eigenvalues of A.
In the book I am reading, the Routh-Hurwitz criterion is then introduced to determine the stability and vibrations of the system. This, apparently, is a more efficient computational reduction than the calculation of eigenvalues.
What are the advantages of using the Routh-Hurwitz criteria for stability and fluctuations, when you can quickly find your own values quickly? For example, will it be useful when I start to study nonlinear dynamics? Is there any additional use that I completely lost?
The Wikipedia article on RH stability analysis has material on control systems, and as a result, a lot of equations are obtained in the s-domain (Laplace transforms), but for my applications I will stay in the time domain for the most part, and just focus rather narrowly on stability and oscillations in linear (or linearized) systems.
: , , - , , , , Matlab.
: Math Exchange, :
https://math.stackexchange.com/questions/690634/use-of-routh-hurwitz-if-you-have-the-eigenvalues
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