Algebraic Methods for Nonlinear Control Systems - download pdf or read online

By Giuseppe Conte, Claude H. Moog, Anna Maria Perdon

ISBN-10: 1846285941

ISBN-13: 9781846285943

ISBN-10: 184628595X

ISBN-13: 9781846285950

It is a self-contained creation to algebraic regulate for nonlinear platforms compatible for researchers and graduate scholars. it's the first booklet facing the linear-algebraic method of nonlinear keep an eye on platforms in this sort of certain and wide style. It presents a complementary method of the extra conventional differential geometry and offers extra simply with numerous very important features of nonlinear structures.

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Extra resources for Algebraic Methods for Nonlinear Control Systems (Communications and Control Engineering)

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This ends the proof of statement (i). 7) for any k ≥ 1. 6. The notion of autonomous element can be defined also in the context of nonexact forms. 10. 1) if there exists an integer ν and meromorphic function coefficients αi in K, for i = 1, . . , ν, so that α0 ω + . . 11. 12. A one form ω in X is an autonomous element if and only if it has an infinite relative degree. Proof. Necessity: Assume that ω in X has an infinite relative degree. 10) This yields that ω is autonomous. Sufficiency: By contradiction, show that if ω has finite relative degree, then it is not autonomous.

Xi+1,j ( ) If ∃ ≥ rij , dyij ∈ Xi+1 , then define sij as the smallest integer such that, abusing the notation, one has locally (r +sij ) yij ij (r +sij ) = yij ij (σ) (y (λ) , yij , u, . . , u(sij ) ) where 0 < λ < r, 0 < σ < rij + sij . 2 (r +s ) • If sij ≥ 0 and ∂ 2 yij ij ij /∂u(sij ) = 0 for some j = 1, . . , 2i−1 , stop! 2 (r +s ) • If Xi+1 + U = Y + U and ∂ 2 yij ij ij /∂u(sij ) = 0, whenever sij ≥ 0, then the algorithm stops and the realization is completed. Otherwise, define (r +s ) the new auxiliary outputs, whenever d(∂yij ij ij /∂u(sij ) ) = 0, respectively, (r ) d(yij ij − (r ∂yij ij +sij ) (sij ) ∂u u) = 0: (r +sij ) yi+1,2j−1 = ∂yij ij , yi+1,2j = ∂u(sij ) (r ) yij ij (r +sij ) − ∂yij ij ∂u(sij ) u End of the algorithm.

Xn ) = J To avoid the introduction of new notations, it is not restrictive to assume γ ≥ max{α+si −1, i = 1, . . , p}. The determinant of J is an analytic function whose set of zeros has an empty interior, so there exists an open dense subset V of IRn+mγ such that det J is different from zero at every point of V and the implicit function theorem applies. Therefore there exist n functions xi = φi (˜ x, u, . . , u(γ) ) for 1 ≤i≤n which define a local diffeomorphism φ parametrized by u, . . 1) becomes 24 2 Modeling ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ x ˜˙ 1 = x ˜2 x ˜˙ 2 = x ˜4 ..

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Algebraic Methods for Nonlinear Control Systems (Communications and Control Engineering) by Giuseppe Conte, Claude H. Moog, Anna Maria Perdon

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