Get Algebraic Methods for Nonlinear Control Systems PDF

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

ISBN-10: 1846285941

ISBN-13: 9781846285943

ISBN-10: 184628595X

ISBN-13: 9781846285950

This can be a self-contained advent to algebraic keep an eye on for nonlinear structures compatible for researchers and graduate scholars. it's the first publication facing the linear-algebraic method of nonlinear keep an eye on structures in this kind of distinctive and wide style. It presents a complementary method of the extra conventional differential geometry and bargains extra simply with a number of vital features of nonlinear platforms.

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Additional info for Algebraic Methods for Nonlinear Control Systems (Communications and Control Engineering)

Sample text

2. 19). 3. Consider the linear system x˙ = Ax + Bu. Compute the spaces Hk , for k ≥ 1, in terms of the matrices A and B and derive the standard controllability criterion for linear systems.

14. The two systems y¨ = u˙ − 2(y˙ − u)2 and ¨ y (3) = u do admit the same irreducible input-output system, y˙ = u. 14). 1, as well as a necessary and sufficient condition for the existence of such a realization. 15 (Realization). 1) yields an input-output equation described by y (κ) = φ(y, . . , y (κ−1) , u, . . 14). 15. 16), to derive a full characterization of the existence of a classical realization. 16. 14) if and only if • • k>s and, Hi is integrable for each i = 1, . . , s + 2. Proof.

Xk ). 24) The assumption k > s indicates that the output y depends only on x. 14). Since the state-space system is proper, necessarily k > s. H1 = spanK {dx, du, . . , du(s) } .. 23), the spaces Hi are integrable as expected. 17. Let y¨ = u˙ 2 , and compute ˙ du, du} ˙ H1 = spanK {dy, dy, H2 = spanK {dy, dy, ˙ du} H3 = spanK {dy, dy˙ − 2udu)} ˙ Since H3 is not integrable, there does not exist any state-space system generating y¨ = u˙ 2 . This can be checked directly, or using some results in [33].

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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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