2.0 METHODOLOGY
The behavior of linear systems, such as those seen in engineering and
physics, can be studied mathematically using eigenvalues. The
eigenvalues of a system can be used to assess a systemβs dynamic
stability and determine whether it is stable or unstable [25]. The
stability of a system is specifically assessed using the eigenvalues of
its state matrix. The system is stable if all the eigenvalues have
negative real portions, which indicates that it will stabilize following
a modest disturbance. The system is unstable if any of the eigenvalues
contain positive real components, which means that it will oscillate
unboundedly in response to slight perturbations [26].
Eigenvalues are the special set of scalar values that are associated
with the set of linear equations most probably in the matrix equations.
The eigenvectors are also termed as Characteristic roots. It is a
nonzero vector that can be changed at most by its scalar factor after
the application of linear transformations. Let π΄ ππ a 2*2 matrix. A
Scaler π is called an eigenvalue of A if there is a nonzero vector π₯Μ
such that Aπ₯Μ
= ππ₯Μ
such a vector π₯Μ
is called an eigenvector of A
corresponding to π [27].