By Jing Zhou, Changyun Wen

From the reviews:

"‘The booklet is beneficial to benefit and comprehend the elemental backstepping schemes’. it may be used as an extra textbook on adaptive regulate for complex scholars. regulate researchers, in particular these operating in adaptive nonlinear keep watch over, also will commonly reap the benefits of this book." (Jacek Kabzinski, Mathematical experiences, factor 2009 b)

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**Additional info for Adaptive backstepping control of uncertain systems: Nonsmooth nonlinearities, interactions or time-variations**

**Example text**

A (y) = ⎢ 0 .. . .. ⎥ = ⎢ .. ⎥ ⎦ ⎣ ⎦ ⎣ T 0 0 . . 20) State Estimation Filters ⎤ ⎡ φa1 0 ⎢ . ⎢ Φa (y) = ⎢ 0 .. ⎣ 0 0 ⎡ ⎤ ΦTa1 (y) ⎢ ⎥ ⎥ ⎢ . ⎥ ⎥ ⎥ == ⎢ .. ⎥ ⎣ ⎦ ⎦ . . φan ΦTan (y) ... . 39 0 .. θ = [bm (t), . . , b0 (t), θa1 (t), . . , θan (t)]T d(t) = [d1 (t), . . , dn (t)] ψ0 (y) = [ψ01 (y), . . 26) k = [k1 , k2 , . . 27) is chosen such that the matrix A0 is strictly stable. 19). We denote the ﬁrst m + 1 columns of Ω T by vm , . . , v1 , v0 and the remaining n columns by Ξ as follows Ω T = [vm , .

T 0 0 . . 20) State Estimation Filters ⎤ ⎡ φa1 0 ⎢ . ⎢ Φa (y) = ⎢ 0 .. ⎣ 0 0 ⎡ ⎤ ΦTa1 (y) ⎢ ⎥ ⎥ ⎢ . ⎥ ⎥ ⎥ == ⎢ .. ⎥ ⎣ ⎦ ⎦ . . φan ΦTan (y) ... . 39 0 .. θ = [bm (t), . . , b0 (t), θa1 (t), . . , θan (t)]T d(t) = [d1 (t), . . , dn (t)] ψ0 (y) = [ψ01 (y), . . 26) k = [k1 , k2 , . . 27) is chosen such that the matrix A0 is strictly stable. 19). We denote the ﬁrst m + 1 columns of Ω T by vm , . . , v1 , v0 and the remaining n columns by Ξ as follows Ω T = [vm , . .

0 ⎥ ⎢ .. ⎥ ⎢ .. ⎥ ⎢ ⎥ ⎥ ⎢ ⎢ . ⎥ . ⎥ .. .. . ⎥ ⎢ ⎥ Ag = ⎢ , Bp = ⎢ . ⎥ , Bg = ⎢ . . ⎥ ⎥ ⎢ ⎢ ⎢ ⎥ ⎢ 0 ⎥ ⎢ B1 ⎥ ⎢ ⎥ ⎦ ⎦ ⎣ ⎣ ⎢ −A1 0 0 . . Ir ⎥ ⎣ ⎦ B0 Bp −A0 0 0 . . 0 Cg = [Ir 0 . . 4) where v is the observability index of G(p), rv = n, Ir is the r × r identity matrix, and Ai ∈ Rr×r , i = 0, . . , v − 1, and Bj ∈ Rr×r , j = 0, . . , m, m ≤ v − 1 are matrices. 5) Bp y = Cg x where x ∈ Rn is the system state, A ∈ Rn×n is the matrix Ag with the ﬁrst r columns equal to zero, Ap ∈ Rn×r are the ﬁrst r columns of Ag and BP Problem Formulation 53 ¯ ∈ R(m+1)r×r , d(t) = [0 Bp ]T d(t) = [dT1 , .