VTechWorks staff will be away for the Thanksgiving holiday beginning at noon on Wednesday, November 22, through Friday, November 24, and will not be replying to requests during this time. Thank you for your patience, and happy holidays!
The problem of determining the stability of a
set of linear differential equations has been of interest to mathematicians and engineers for a considerable length of time.
The problem is attacked by obtaining the characteristic equation of the original set of equations and determining the stability of this equation.
The stability of the characteristic equation is
first considered in terms of a continued fraction expansion.
Necessary and sufficient conditions are given for
the characteristic equation to be stable.
The stability of the equation is then determined by means of a determinant sequence, which was the manner
originally presented by A. Hurwitz in 1895.
The Nyquist criterion, which is a graphical method
for determining whether the equation is stable, is then
An example is given for each of the above methods to
illustrate the procedure used in determining whether the
equation is stable or unstable. Also included is a brief
analysis of stability for non-linear equations.