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

This is a self-contained advent to algebraic keep an eye on for nonlinear platforms appropriate for researchers and graduate scholars. it's the first booklet facing the linear-algebraic method of nonlinear regulate platforms in any such distinctive and huge model. It presents a complementary method of the extra conventional differential geometry and bargains extra simply with a number of vital features of nonlinear systems.

Show description

Read Online or Download Algebraic methods for nonlinear control systems PDF

Best system theory books

Controlled and Conditioned Invariants in Linear System Theory

Utilizing a geometrical method of process concept, this paintings discusses managed and conditioned invariance to geometrical research and layout of multivariable keep an eye on structures, proposing new mathematical theories, new methods to straightforward difficulties and utilized arithmetic themes.

Boolean Constructions in Universal Algebras

Over the last few a long time the information, tools, and result of the speculation of Boolean algebras have performed an expanding function in quite a few branches of arithmetic and cybernetics. This monograph is dedicated to the basics of the idea of Boolean buildings in common algebra. additionally thought of are the issues of providing assorted kinds of common algebra with those structures, and functions for investigating the spectra and skeletons of types of common algebras.

Advanced H∞ Control: Towards Nonsmooth Theory and Applications

This compact monograph is targeted on disturbance attenuation in nonsmooth dynamic structures, constructing an H∞ method within the nonsmooth atmosphere. just like the traditional nonlinear H∞ technique, the proposed nonsmooth layout promises either the interior asymptotic balance of a nominal closed-loop method and the dissipativity inequality, which states that the dimensions of an blunders sign is uniformly bounded with recognize to the worst-case dimension of an exterior disturbance sign.

Mathematical Systems Theory I: Modelling, State Space Analysis, Stability and Robustness (Pt. 1)

This e-book provides the mathematical foundations of platforms thought in a self-contained, accomplished, designated and mathematically rigorous means. this primary quantity is dedicated to the research of dynamical structures, while the second one quantity can be dedicated to keep watch over. It combines beneficial properties of an in depth introductory textbook with that of a reference resource.

Additional resources for Algebraic methods for nonlinear control systems

Example text

H1 1 If (s −1) (sj ) ; . . ; h j , . . , hj ∂x (s ) ) j−1 j−1 ∂(h1 , . . , hj−1 ) ∂(h1 , . . , hj−1 = rank ∂x ∂x we define sj = 0. Write K = s1 + . . + sp . The vector rank −1) , hj ) S = (h1 , . . , h1s1 −1 , . . , hp , . . 1 State Elimination 23 It will be established in Chapter 4 that the case K < n corresponds to nonobservable systems. In this case, there exist analytic functions g1 (x), . . , gn−K (x) such that the matrix J = ∂(S, g1 , . . , gn−K ) ∂x has full rank n. Then the system of equations ⎧ x ˜1 = h1 (x, u, .

U2 Compute H1 = spanK {dx} H2 = spanK {(sin x3 )dx1 − (cos x3 )dx2 } H3 = 0 The controllability indices are computed as follows. h1 = 2, h2 = 1, h3 = 0, . . and k1∗ = 2, k2∗ = 1. However, there does not exist any change of coordinates that gives rise to a representation containing a Brunovsky block of dimension 2. The system is accessible; there does not exist any autonomous element. 52 3 Accessibility ✻ u1 ✒ ✩ ✛ ❅ ✛✘ x3 ❅ ❅ u2 ✚ ✲❅ ❅ ❅ x2 ✲ 0 x1 Fig. 2. 21. Consider ⎞ ⎛ 1 x˙ 1 ⎜ x˙ 2 ⎟ ⎜ x3 ⎟ ⎜ ⎜ ⎜ x˙ 4 ⎟ ⎜ x4 ⎟ ⎜ ⎜ ⎟ = ⎜ ..

1 State Elimination 23 It will be established in Chapter 4 that the case K < n corresponds to nonobservable systems. In this case, there exist analytic functions g1 (x), . . , gn−K (x) such that the matrix J = ∂(S, g1 , . . , gn−K ) ∂x has full rank n. Then the system of equations ⎧ x ˜1 = h1 (x, u, . . , u(α) ) ⎪ ⎪ ⎪ .. ⎪ ⎪ ⎪ . ⎪ ⎪ ⎪ (s −1) ⎪ ⎪ = h1 1 (x, u, . . , u(α+s1 −1) ) x ˜ s1 ⎪ ⎪ ⎪ ⎪ x ˜s1 +1 = h2 (x, u, . . , u(α) ) ⎪ ⎨ .. ⎪ ⎪ (s −1) ⎪ ⎪ = h2 2 (x, u, . . , u(α+s2 −1) ) x ˜ s1 +s2 ⎪ ⎪ ⎪ ..

Download PDF sample

Rated 4.69 of 5 – based on 24 votes