A second order LTI system is described by the following state equations
\[\frac{{\rm{d}}}{{{\rm{dt}}}}\] x₁(t) - x₂(t) = 0
\[\frac{{\rm{d}}}{{{\rm{dt}}}}\] x₂(t) + 2x₁(t) + 3x₂(t) = r(t) where x₁(t) and x₂(t) are the two state variables and r(t) denotes the input. The output c(t) = x₁(t).
The system is