Introduction to State Space
In a state space representation we end up with a first order matrix differential equation:
Potentially problematic things
By defining a system in state space form we can change an nth order differential equation (or transfer function) into n first order differential equations of the form:
where x is an n element column vector, y is the output and u is the input. The formulation above is for a single-input single-output (SISO) system. The input u can be a vector, as can the output y (either one makes the element "d" a matrix).
We discussed various manipulations that we can do with State Space representations of systems.
Note, your book does everything in terms of P, Matlab uses T, where T=P-1.