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By Soloff-levy Barbara

This nice e-book explains what fabrics are invaluable for drawing and demonstrates easy methods to create ogres, fairies, elves, unicorns, dragons, and wizards.

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Let ν 0 = (ν01 , . . , ν0l ) ∈ ν with 0 ≤ ν0i < 1, and then there exist the unique ξ0i ’s such that ν0i = (1 − ξ0(i−1) ) l−1 j=i ξ0 j , which is obtained in the following recursive manner: 4 Motion Control Using an H∞ -Control-Based Approach 32 ξ0(l−1) = 1 − ν0l 1 ξ0(l−2) = 1 − ξ0(l−1) ν0(l−1) .. 1 ξ01 = 1 − ξ0(l−1) ξ0(l−2) ···ξ02 ν02 and 0 < ξ0i ≤ 1 is easily confirmed. Next, let us consider the case where ν0s = 1 (1 ≤ s ≤ l) and ν0i = 0 (i = s). In this case, by setting ξ0(s−1) = 0 and ξ0i = 1 (i = s−1, 0), ν0i can be represented by the same form ν0i = (1−ξ0(i−1) ) l−1 j=i ξ0 j .

7) where σ¯ (·) denotes the largest singular value. If there exists no Δ ∈ which makes the matrix singular, then μ (M) := 0. Furthermore, this notion can be extended to a linear time-invariant system matrix M(s) ∈ Cn×n as μ (M(s)) := sup μ (M(iω)). 8) The method to analyze robustness of the system using μ instead of ||M(s)||∞ = supω∈R (σ¯ /M(iω)) (when M(s) ∈ H∞ ) is called “μ-analysis”. As described above, when evaluating the robust stability of the feedback configuration of the structured Δ and Fl (M, K ), the method using only their H∞ norms will provide a conservative result.

The second one requires a control design method with which one can cope with robustness. When these two features are accounted for, the H∞ control framework can be naturally a powerful candidate. The H∞ © Springer International Publishing Switzerland 2016 M. 1007/978-3-319-21780-2_4 21 22 4 Motion Control Using an H∞ -Control-Based Approach control that we have employed is fundamentally for linear time-invariant systems. However, by adding some modifications, the nonlinearity can be reduced and be absorbed into the model uncertainty.

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