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A weighting pattern for a linear dynamical system describes the relationship between an input u {\displaystyle u} and output y {\displaystyle y}. Given the time-variant system described by
then the output can be written as
where T {\displaystyle T} is the weighting pattern for the system. For such a system, the weighting pattern is T = C ϕ B {\displaystyle T=C\phi B} such that ϕ {\displaystyle \phi } is the state transition matrix.
The weighting pattern will determine a system, but if there exists a realization for this weighting pattern then there exist many that do so.
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