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.[1]
Linear time invariant system
In a LTI system then the weighting pattern is:
- Continuous
where is the matrix exponential.
- Discrete
- .
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References
- Brockett, Roger W. (1970). Finite Dimensional Linear Systems. John Wiley & Sons. ISBN 978-0-471-10585-5.
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