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 [ A ( t ) , B ( t ) , C ( t ) , D ( t ) ] {displaystyle } such that 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 } such that with ( u ( t ) , y ( t ) ) {displaystyle (u(t),y(t))} describing the input and output of the system at time t {displaystyle t} . For a linear time-invariant system specified by a transfer matrix, H ( s ) {displaystyle H(s)} , a realization is any quadruple of matrices ( A , B , C , D ) {displaystyle (A,B,C,D)} such that H ( s ) = C ( s I − A ) − 1 B + D {displaystyle H(s)=C(sI-A)^{-1}B+D} . Any given transfer function which is strictly proper can easily be transferred into state-space by the following approach (this example is for a 4-dimensional, single-input, single-output system)):