  This paper focuses on the mathematical approaches to the analysis of
stability that is a crucial step in the design of dynamical systems. Three
methods are presented, namely, absolutely integrable impulse response, Fourier
integral, and Laplace transform. The superiority of Laplace transform over the
other methods becomes clear for several reasons that include the following: 1)
It allows for the analysis of the stable, as well as, the unstable systems. 2)
It not only determines absolute stability (a yes/no answer), but also shines
light on the relative stability (how stable/unstable the system is), allowing
for a design with a good degree of stability. 3) Its algebraic and convolution
properties significantly simplify the mathematical manipulations involved in
the analysis, especially when tackling a complex system composed of several
simpler ones. A brief relevant introduction to the subject of systems is
presented for the unfamiliar reader. Additionally, appropriate physical
concepts and examples are presented for better clarity.
