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

This is a self-contained creation to algebraic keep watch over for nonlinear structures compatible for researchers and graduate scholars. it's the first booklet facing the linear-algebraic method of nonlinear keep an eye on platforms in one of these particular and broad model. It presents a complementary method of the extra conventional differential geometry and bargains extra simply with numerous very important features of nonlinear systems.

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U(γ) ) .. ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ x ˜˙ s1 +···+sp ⎪ ⎪ ⎪ ˙ ⎪ x ˜ ⎪ s1 +···+sp +i ⎪ ⎪ ⎪ y1 ⎪ ⎪ ⎪ ⎪ y ⎪ 2 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ yp = = = = .. 5) (s ) hp p (φ(˜ x), u, . . , u(γ) ) gi (˜ x), u, . . , u(γ) ) i = 1, . . , i ∂x ∂x so that (s ) ∂hi i = [c1 . . cs1 +···+si 0 . . 0]J ∂∂x x ˜j ∂x ˜ = [c1 . . cs1 +···+si 0 . . 0] ej = 0 j > s1 + · · · + s i where ej is the jth column of the identity matrix. Therefore the functions (s ) x), u, . . , u(γ) ) depend only on x ˜1 , . . +si . hi i (φ(˜ Since the following identities hold, y1 = x˜1 , y˙ 1 = x˜2 , .

Thus, φ = y˙ − u = 0 is an irreducible input-output system of y¨ = u˙ + (y˙ − u)2 . It is not true that any input-output system has an irreducible input-output system. 9. 19) is not irreducible. Let φ = y/u ˙ = 0, which is not an irreducible input-output system in the sense of the above Definition. 19) does not admit any irreducible input-output system. In the special case of linear time-invariant systems, the reduction procedure corresponds to a pole/zero cancellation in the transfer function. For nonlinear systems, the above procedure also generalizes the so-called primitive step in [28].

Part of the healthy CD4 cells will be converted into infected CD4 cells. It is supposed to be proportional to both the T population and the v population. Finally, the dynamics of T is T˙ = s − δT − βT v The population T ∗ of infected CD4 cells is also submitted to a natural death, with a lifetime 1/μ. The only source of production of new infected CD4 cells has already been described and its rate equals βT v. Thus, the dynamics of T ∗ reads as T˙ ∗ = βT v − μT ∗ The population v of HIV virions is submitted to a natural death and their lifetime equals 1/c.

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Algebraic methods for nonlinear control systems by Giuseppe Conte, Claude H. Moog, Anna Maria Perdon


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