Weighting pattern


A weighting pattern for a linear dynamical system describes the relationship between an input and output. Given the time-variant system described by
then the output can be written as
where is the weighting pattern for the system. For such a system, the weighting pattern is such that 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.

Linear time invariant system

In a LTI system then the weighting pattern is:
; Continuous
where is the matrix exponential.
; Discrete