System realization

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

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

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