By Jinzhi Wang, Zhisheng Duan, Ying Yang, Lin Huang
Nonlinear platforms with desk bound units are vital simply because they hide loads of sensible platforms in engineering. earlier research has been in response to the frequency-domain for this classification of platforms. despite the fact that, few effects on robustness research and controller layout for those structures are simply available.
This ebook offers the research in addition to equipment according to the worldwide houses of platforms with desk bound units in a unified time-domain and frequency-domain framework. the focal point is on multi-input and multi-output structures, in comparison to prior guides which thought of purely single-input and single-output platforms. The regulate tools awarded during this booklet could be important for study on nonlinear structures with desk bound sets.
Contents: Linear structures and Linear Matrix Inequalities; LMI method of H keep an eye on; research and keep watch over of confident genuine structures; Absolute balance and Dichotomy of Lur e structures; Pendulum-Like suggestions platforms; Controller layout for a category of Pendulum-Like platforms; Controller Designs for platforms with enter Nonlinearities; research and regulate for doubtful suggestions Nonlinear platforms; keep an eye on of Periodic Oscillations in Nonlinear platforms; Interconnected structures; Chua s Circuits.
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Extra info for Analysis And Control Of Nonlinear Systems With Stationary Sets: Time-Domain and Frequency-Domain Methods
1. Assume that there exists some x0 such that F1 (x0 ) > 0. Then F0 (x) ≥ 0 for all x such that F1 (x) ≥ 0 if and only if there exists τ ≥ 0 such that for all x, F0 (x) − τ F1 (x) ≥ 0. 2 The S-procedure for strict inequalities Consider another form of the S-procedure which involves quadratic forms and strict inequalities. Let F0 , F1 , · · · , Fp ∈ Rn×n be symmetric matrices. We still consider the following conditions. (I) xT F0 x > 0 for all x ∈ Rn , x = 0 such that xT Fi x ≥ 0, i = 1, · · · , p.
The projection lemma for strict and nonstrict inequalities [Boyd et al. (1994); Gahinet (1992); Iwasaki and Skelton (1994); Helmersson (1995); Skelton and Iwasaki (1995)] are used to eliminate variables in certain matrix inequalities. It dates back to the Finsler’s Lemma [Finsler (1937)]. It is also related to the S-procedure. A survey article on S-procedure is by [Uhlig (1979)], see also [Horn and Johnson (1991); Yakubovich (1971, 1973a); Fradkov and Yakubovich (1979); Huang (2003)] for proofs of various S-procedure results.
G. [Gahinet (1992); Iwasaki and Skelton (1994); Boyd et al. (1994)]. 1 (Projection lemma). Let matrices U, V and Q be given. Suppose that rank(U ) < n and rank(V ) < n. 21) holds. 21) holds and V T V > 0, then 1 1 G = −ρU T ΦV Υ + Ω 2 F Υ 2 , ||F || < ρ, where scalar ρ and the matrix F are free parameters, and −1 1 > 0, Φ := U U T − Q ρ Ω := I − U T (Φ − ΦV ΥV T Φ)U, Υ := (V T ΦV )−1 . 4. 20), the details can be found in [Skelton and Iwasaki (1995)]. 5. 21) disappears [Boyd et al. (1994)]. Next, we consider non-strict LMI Q + U GV T + V GT U T ≤ 0.