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Pattern in control theory
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
- .
References