Get Active disturbance rejection control for nonlinear systems : PDF

By Bao-Zhu Guo, Zhi-Liang Zhao

ISBN-10: 1119239931

ISBN-13: 9781119239932

ISBN-10: 111923994X

ISBN-13: 9781119239949

ISBN-10: 1119239958

ISBN-13: 9781119239956

A concise, in-depth advent to lively disturbance rejection keep watch over conception for nonlinear platforms, with numerical simulations and obviously labored out equations

  • Provides the basic, theoretical starting place for functions of lively disturbance rejection control
  • Features numerical simulations and obviously labored out equations
  • Highlights the benefits of energetic disturbance rejection keep watch over, together with small overshooting, quick convergence, and effort savings

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All these steps are accomplished by a series of lemmas. 95) for which the proof is omitted. 11. 95) and b > 0. 95) with x(t0 ) = x0 satisfying ∞ ∞. ≤ b. Then there exists a solution x(t) of x(t) − y(t)|∞ ≤ x0 − y(t0 ) eK|t−t0 | as long as x0 − y(t0 ) eK|t−t| ≤ b. 11, we need firstly to regularize F (t, x). To facilitate the construction of a Lyapunov function that is smooth up to t = 0, we extend F (t, x) on [−1, 0) × Rn by setting F (t, x) = { − x}. It is easy to verify that if F (t, x) is a nonempty convex compact set for any (t, x) ∈ ([0, ∞) \ N0 ) × Rn , then, after the extension, it is also a nonempty convex compact set for any (t, x) ∈ ([−1, ∞) \ N0 ) × Rn .

Ain ), Eij = ei ej , Eij = ei ⊗ ej . −−−→ → − (iv) Let A ∈ Rn×m , B ∈ Rm×s , and C ∈ Rs×l . Then ABC = (A ⊗ C ) B . Let A, C ∈ Rn×n . 58) A X + XA = C. 58). 2 Let A, C ∈ Rn×n . 58). 2 (ii) There exists a unique vector x ∈ Rn satisfying the linear equation − → (A ⊗ In×n + In×n ⊗ A )x = C . 59) (iii) The matrix A ⊗ In×n + In×n ⊗ A is invertible, that is, rank(A ⊗ In×n + In×n ⊗ A ) = n2 . (iv) ni,j=1 (λi + λj ) = 0. 5. 5 If A is a Hurwitz matrix, that is, all the eigenvalues of A have the negative real part, then for any positive definite symmetrical matrix C ∈ Rn×n there is a unique positive definite symmetrical matrix solution X ∈ Rn×n to the Lyapunov equation: A X + XA = −C.

For the sake of simplicity and without loss of generality, we may assume that Ω = Rn . 87) is finite-time stable, it is asymptotically stable. 3, there exists a positive definite Lyapunov function V˜ : Rn → R such that LF V˜ is negative definite on Rn . 88) 1, s ∈ [2, +∞), and ⎧ ⎪ ⎨ V (x) = +∞ 0 ⎪ ⎩0, 1 μk+1 (α ◦ V˜ )(μr1 x1 , . . 89) x = 0. Apparently, V (x) is positive definite. For any λ > 0, x = 0, +∞ V (λr1 x1 , . . , λrn xn ) = 1 μk+1 0 +∞ = λk 0 (α ◦ V˜ )((λμ)r1 x1 , . . , (λμ)rn xn )dμ 1 (α ◦ V˜ )((λμ)r1 x1 , .

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Active disturbance rejection control for nonlinear systems : an introduction by Bao-Zhu Guo, Zhi-Liang Zhao


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