Realization (systems)
Systems theory
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Realization (systems)
Systems theory
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 [ A ( t ) , B ( t ) , C ( t ) , D ( t ) ] {\displaystyle [A(t),B(t),C(t),D(t)]} such that x ˙ ( t ) = A ( t ) x ( t ) + B ( t ) u ( t ) {\displaystyle {\dot {\mathbf {x} }}(t)=A(t)\mathbf {x} (t)+B(t)\mathbf {u} (t)} y ( t ) = C ( t ) x ( t ) + D ( t ) u ( t ) {\displaystyle \mathbf {y} (t)=C(t)\mathbf {x} (t)+D(t)\mathbf {u} (t)} with...
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From Wikipedia
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 [ A ( t ) , B ( t ) , C ( t ) , D ( t ) ] {\displaystyle [A(t),B(t),C(t),D(t)]} such that x ˙ ( t ) = A ( t ) x ( t ) + B ( t ) u ( t ) {\displaystyle {\dot {\mathbf {x} }}(t)=A(t)\mathbf {x} (t)+B(t)\mathbf {u} (t)} y ( t ) = C ( t ) x ( t ) + D ( t ) u ( t ) {\displaystyle \mathbf {y} (t)=C(t)\mathbf {x} (t)+D(t)\mathbf {u} (t)} with ( u ( t ) , y ( t ) ) {\displaystyle (u(t),y(t))} describing the input and output of the system at time t {\displaystyle t} .
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