(I apologize for the late post. I still have another one for today to deliver.)

While walking to work today I began to remember about Linear time-invariant theory, which can be said to be the mainstay of control theory. Any system that Linear time invariant theory is fully applicable to are called LTI systems. LTI theory is an ideal place to start. Any LTI system are linearity and time invariance. These make analysis of such system independent of the physical properties of the system and allow a whole host of techniques to be usable on them.

LTI systems are completely describable by their impulse response and frequency response. They are also easy to model and have many tools to simplify this process.

So I will start there and dive into the mathematics of it in the process.