Statespace vs ode45

When is it best to model a dynamic system using just the differential equations and ode45 solver, versus decomposing the differential equations into a statespace form (with A, B, C, D matricies). It seems as though the statespace form is significantly more powerful interms of understanding controllablity and still can give you the same information that ode45 would provide.

Answer 1

[Star Strider]

Use the differential integration solvers if you have a nonlinear system, and particularly a nonlinear system that you cannot successfully linearize. If you have a linear system, use ‘ABCD’ matrices. Also, for a linear system, you can use the expm function to integrate the ‘A’ matrix. See any book on linear control systems for guidance on that.