仿射非线性系统 

仿射系统是输入为线性的非线性系统. 其可以用多种方法指定，并且可以被转换为其他系统模型.

用常微分方程（ODE）指定一个系统.

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X AffineStateSpaceModel[m x''[t] + c[x] x'[t] + k[x] == F[t], x[t], F[t], x[t], t]

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用系统分量指定系统.

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X AffineStateSpaceModel[{{Subscript[f, 1][Subscript[x, 1], Subscript[x, 2]], Subscript[f, 2][Subscript[x, 1], Subscript[x, 2]]}, {{Subscript[g, 11][Subscript[x, 1], Subscript[x, 2]]}, {Subscript[g, 21][Subscript[x, 1], Subscript[x, 2]]}}, {Subscript[h, 1][Subscript[x, 1], Subscript[x, 2]]}}, {Subscript[x, 1], Subscript[x, 2]}]

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从其他系统模型获得的系统.

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X AffineStateSpaceModel /@ {StateSpaceModel[{{{Subscript[a, 11], Subscript[a, 12]}, {Subscript[a, 21], Subscript[a, 22]}}, {{Subscript[b, 11]}, {Subscript[b, 21]}}, {{Subscript[c, 11], Subscript[c, 12]}}, {{0}}}, {Subscript[x, 1], Subscript[x, 2]}, SamplingPeriod ->None, SystemsModelLabels -> None], TransferFunctionModel[{{{1}}, (-2) s + s^2}, s], NonlinearStateSpaceModel[ {{Subscript[f, 1][Subscript[x, 1], Subscript[x, 2]] + Subscript[u, 1] Subscript[g, 11][Subscript[x, 1], Subscript[x, 2]], Subscript[f, 2][Subscript[x, 1], Subscript[x, 2]] + Subscript[u, 1] Subscript[g, 21][Subscript[x, 1], Subscript[x, 2]]}, {Subscript[ h, 1][Subscript[x, 1], Subscript[x, 2]]}}, {Subscript[x, 1], Subscript[x, 2]}, {Subscript[u, 1]}, {Automatic}, Automatic , SamplingPeriod -> None]}

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输入为非线性 NonlinearStateSpaceModel 是近似的.

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X AffineStateSpaceModel[ NonlinearStateSpaceModel[ {{Subscript[f, 1][Subscript[x, 1], Subscript[x, 2], Subscript[u, 1]], Subscript[f, 2][Subscript[x, 1], Subscript[x, 2], Subscript[u, 1]]}, {Subscript[h, 1][Subscript[x, 1], Subscript[x, 2], Subscript[ u, 1]]}}, {Subscript[x, 1], Subscript[x, 2]}, {Subscript[u, 1]}, {Automatic}, Automatic , SamplingPeriod -> None]]

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线性 AffineStateSpaceModel 被精确转换为线性系统模型.

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X assm = AffineStateSpaceModel[ {{Subscript[x, 1] + Subscript[x, 2], Subscript[x, 1]}, {{ 1 }, {1 }}, {Subscript[x, 1]}, {{ 0 }}}, {Subscript[x, 1], Subscript[x, 2]}, Automatic, {Automatic}, Automatic , SamplingPeriod -> None];

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X {StateSpaceModel[assm], TransferFunctionModel[assm]}

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通常，仿射模型在转换为线性系统模型是被近似.

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X assm = AffineStateSpaceModel[ {{Subscript[x, 1] + Subscript[x, 2] + Subscript[x, 1] Subscript[x, 2], Subscript[x, 1]}, {{ 1 }, {1 + Subscript[x, 2] }}, {Subscript[x, 1]}, {{ 0 }}}, {Subscript[x, 1], Subscript[x, 2]}, Automatic, {Automatic}, Automatic , SamplingPeriod -> None];

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X {StateSpaceModel[assm], TransferFunctionModel[assm]}

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转换为 NonlinearStateSpaceModel 是精确的.

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X NonlinearStateSpaceModel[ AffineStateSpaceModel[ {{Subscript[f, 1][Subscript[x, 1], Subscript[ x, 2]], Subscript[f, 2][Subscript[x, 1], Subscript[x, 2]]}, {{ Subscript[g, 11][Subscript[x, 1], Subscript[x, 2]] }, {Subscript[g, 21][Subscript[x, 1], Subscript[x, 2]] }}, {Subscript[h, 1][Subscript[x, 1], Subscript[x, 2]]}, {{ 0 }}}, {Subscript[x, 1], Subscript[x, 2]}, {Subscript[u, 1]}, {Automatic}, Automatic , SamplingPeriod -> None] ]

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