TABLE OF CONTENTS When controlling a system using the techniques of classical control one generally uses the system's output in the feedback. In this way one can improve the gain and phase margins, make the system faster, and generally improve the system's performance.
When controlling a system using the techniques of modern control, one can (generally) do much more than just improve the margins; one can place the system's poles as one pleases. This improvement, however, comes at a price. In order to place the poles of the system, one must generally know the complete internal state of the system. This is often not a trivial task.
In classical control, one generally describes a system using high-order differential equations or, equivalently, a transfer function. In modern control we use systems of first order equations. We consider systems that have a single input, u( t), a single output, y( t), but many states. To describe systems, we make use of one matrix, A and three vectors, 
which is the vector that is made up of the system's states, and the vectors 
and 
. The equations that describe the evolution of the system's states and the system's output must be put in the form:
The first equation describes the evolution of the state of the system and is called the state equation. The second equation gives the output as a linear combination of the states.
Let us consider a simple...
