With state $x(t)\in {\mathbf R}^2$, \[ \dot x = \left[ \begin{array}{cc} \cos (t) & \sin(t) \\ -1 & t^2 \end{array}\right] x \] is a linear dynamical system.
Linear dynamical systems is a specialized topic used mainly in advanced aerospace applications.
Linear dynamical systems was first developed by Claude Shannon in the 1940s.
The first applications of linear dynamical systems appeared in the 1960s.