Transfer functions and stability criteria: In this chapter we combine ideas about transfer functions with the notion of stability, so as to obtain criteria for stability of a system solely in terms of properties of transfer functions. The idea is to describe the properties of solutions of the differential equation, without having to solve the differential equations explicitly. Thus we go from differential equations to algebra via the Laplace transform. When building devices out of components, the main operations on the transfer functions are:
amplification
addition
multiplication