# Technological theory of social production

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 note that if there exists a realization for this weighting pattern then there exists many that do so.^{[1]}

## Linear time invariant system

In a LTI system then the weighting pattern is:

where is the matrix exponential.

## References

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