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Controlled invariant subspace : ウィキペディア英語版
Controlled invariant subspace
In control theory, a controlled invariant subspace of the state space representation of some system is a subspace such that, if the state of the system is initially in the subspace, it is possible to control the system so that the state is in the subspace at all times. This concept was introduced by Giuseppe Basile and Giovanni Marro .
== Definition ==
Consider a linear system described by the differential equation
: \dot(t) + B\mathbf(t).
Here, x(''t'') ∈ R''n'' denotes the state of the system and u(''t'') ∈ R''p'' is the input. The matrices ''A'' and ''B'' have size ''n'' × ''n'' and ''n'' × ''p'' respectively.
A subspace ''V'' ⊂ R''n'' is a ''controlled invariant subspace'' if for any x(0) ∈ ''V'', there is an input u(''t'') such that x(''t'') ∈ ''V'' for all nonnegative ''t''.

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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