Introduction to State Space

In a state space representation we end up with a first order matrix differential equation:

                    
                    

Good things:

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.