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 system’s 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 𝐴 𝑏𝑒 a 2*2 matrix. A Scaler πœ† is called an eigenvalue of A if there is a nonzero vector π‘₯Μ… such that Aπ‘₯Μ… = πœ†π‘₯Μ… such a vector π‘₯Μ… is called an eigenvector of A corresponding to πœ† [27].