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## A criterion for the differential flatness of a nonlinear control system

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1
Bruno Sauvalle

#### Résumé

Let's consider a control system described by the implicit equation F (x, ˙ x) = 0. If this system is differentially flat, then the following criterion is satisfied : For some integer r, there exists a function ϕ(y0, y1, .., yr) satisfying the following conditions: (1) The map (y0, .., yr+1) → (ϕ(y0, y1, .., yr), ∂ϕ/ ∂y0 y1 + ∂ϕ/ ∂y1 y2 + .. + ∂ϕ/ ∂yr yr+1) is a submersion on the variety F (x, p) = 0. (2) The map y0 → x0 = ϕ(y0, 0, .., 0) is a diffeomorphism on the equilibrium variety F (x, 0) = 0. Inversely, if a control system satifies this flatness criterion, then it is locally controllable at equilibrium points.

### Dates et versions

hal-01631061 , version 1 (09-11-2017)

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• HAL Id : hal-01631061 , version 1
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### Citer

Bruno Sauvalle. A criterion for the differential flatness of a nonlinear control system. 2017. ⟨hal-01631061⟩

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