# Infinite State Systems

We study state machines with

*States* = *Reals ^{ N}*

*Inputs *= *Reals ^{ M}*

*Outputs* = *Reals ^{K}*

The number of states and the sizes of the input and output alphabets are infinite, which tends to make things more complicated. However, these sets now have arithmetic properties, which opens up a huge new range of modeling and analysis possibilities.

A **block diagram **of such a system shows the input coming over *M *input
ports and the output delivered over *K* output ports. (MIMO stands for
multi-input, multi-output.)