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Weighting pattern : ウィキペディア英語版
Weighting pattern
A weighting pattern for a linear dynamical system describes the relationship between an input u and output y. Given the time-variant system described by
: \dot(t) = A(t)x(t) + B(t)u(t)
: y(t) = C(t)x(t),
then the output can be written as
: y(t) = y(t_0) + \int_^t T(t,\sigma)u(\sigma) d\sigma,
where T(\cdot,\cdot) is the weighting pattern for the system. For such a system, the weighting pattern is T(t,\sigma) = C(t)\phi(t,\sigma)B(\sigma) such that \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.
==Linear time invariant system==
In a LTI system then the weighting pattern is:
; Continuous
: T(t,\sigma) = C e^ B
where e^ is the matrix exponential.
; Discrete
: T(k,l) = C A^ B.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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