# StateTransformationLinearize - references?

I am impressed by StateTransformationLinearize, and I feel terribly bad for not having noticed this function before.

How does it work?

Does it attempt to find a $$C^r$$-conjugate of the system? If so, how does it do this?

Why can't it handle Affine State Space Models with symbolic parameters?

For instance, slight changes in the coefficients of the featured examples, lead to failures in finding the transformation. Perhaps if I would figure out how this straightening is done, I could grasp something more about its applicability.

Example

    sys=AffineStateSpaceModel[{{4*Subscript[x, 1], 7*Subscript[x, 1]^2 + Subscript[x, 2]}, {{1}, {-1 + 2*Subscript[x, 1]}}, {Subscript[x, 2]}, {{0}}}, {Subscript[x, 1], Subscript[x, 2]},
{{Subscript[\[FormalU], 1], 0}}, {Automatic}, Automatic, SamplingPeriod -> None];


This is an example taken from the documentation. If you change the first coefficient, into a different number, i.e.:

sys=AffineStateSpaceModel[{{3*Subscript[x, 1], 7*Subscript[x, 1]^2 + Subscript[x, 2]}, {{1}, {-1 + 2*Subscript[x, 1]}}, {Subscript[x, 2]}, {{0}}}, {Subscript[x, 1], Subscript[x, 2]},
{{Subscript[\[FormalU], 1], 0}}, {Automatic}, Automatic, SamplingPeriod -> None];


It already fails to find the transformation:

test = StateTransformationLinearize[ sys, {{Subscript[z, 1], Subscript[z, 2]}, "InputState"}];

Outputting the following error msg:

ControlStateAndFeedbackLinearizationsDumpStateSpaceLinarize::nclin: -- Message text not found -- (input-state)

• It would be helpful to have examples that work or fail, respectively, to find the transformation in question. – Daniel Lichtblau Mar 31 '19 at 13:43
• OK. I'll add an example right now. – Mirko Aveta Mar 31 '19 at 13:55
• Linearize is misspelled in the message -- odd since it is the message head. – Michael E2 Mar 31 '19 at 17:21
• You can inspect some methods via ?**Linearize*. The misspelling comes from ControlStateAndFeedbackLinearizationsDumpssLinearize0` – Michael E2 Mar 31 '19 at 17:40