The only stable normal forms of affine systems under feedback are linear (Q1101052)
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scientific article; zbMATH DE number 4045586
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The only stable normal forms of affine systems under feedback are linear |
scientific article; zbMATH DE number 4045586 |
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The only stable normal forms of affine systems under feedback are linear (English)
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1987
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It is shown for which ranges of dimensions (m,n) smooth affine control systems \(\dot x=f(x)+\sum^{m}_{i=1}u_ ig_ i(x)\), \(x\in {\mathbb{R}}^ n\), possess structurally stable normal forms with respect to the static feedback group. Such stable forms exist only if \(m=n\) or if \(m=1\) and \(n=2\) and are, in these cases, linear.
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Lie group
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structural stability
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smooth affine control systems
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structurally stable normal forms
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static feedback
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