Realization (systems)

In systems theory, a realization of a state space model is an implementation of a given input-output behavior. That is, given an input-output relationship, a realization is a quadruple of (time-varying) matrices ${\displaystyle [A(t),B(t),C(t),D(t)]}$ such that

${\displaystyle {\dot {\mathbf {x} }}(t)=A(t)\mathbf {x} (t)+B(t)\mathbf {u} (t)}$

${\displaystyle \mathbf {y} (t)=C(t)\mathbf {x} (t)+D(t)\mathbf {u} (t)}$

with ${\displaystyle (u(t),y(t))}$ describing the input and output of the system at time ${\displaystyle t}$.