Analysis And Control Of Nonlinear Systems With Stationary by Jinzhi Wang, Zhisheng Duan, Ying Yang, Lin Huang

By Jinzhi Wang, Zhisheng Duan, Ying Yang, Lin Huang

Nonlinear platforms with desk bound units are very important simply because they disguise loads of functional structures in engineering. prior research has been in response to the frequency-domain for this category of structures. even though, few effects on robustness research and controller layout for those platforms are simply available.
This e-book offers the research in addition to tools according to the worldwide homes of structures with desk bound units in a unified time-domain and frequency-domain framework. the focal point is on multi-input and multi-output platforms, in comparison to prior courses which thought of in simple terms single-input and single-output structures. The keep watch over tools offered during this publication may be helpful for study on nonlinear platforms with desk bound sets.
Contents: Linear platforms and Linear Matrix Inequalities; LMI method of H keep an eye on; research and keep an eye on of confident actual platforms; Absolute balance and Dichotomy of Lur e platforms; Pendulum-Like suggestions structures; Controller layout for a category of Pendulum-Like structures; Controller Designs for platforms with enter Nonlinearities; research and regulate for doubtful suggestions Nonlinear platforms; keep watch over of Periodic Oscillations in Nonlinear structures; Interconnected platforms; Chua s Circuits.

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Additional info for Analysis And Control Of Nonlinear Systems With Stationary Sets: Time-Domain and Frequency-Domain Methods

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2. Assume that there exists some x0 such that xT0 F1 x0 > 0. Then xT F0 x > 0 for all x = 0 such that xT F1 x ≥ 0 if and only if there exists τ ≥ 0 such that for all x = 0, xT F0 x − τ xT F1 x > 0. 5 Kalman-Yakuboviˇ c-Popov (KYP) lemma and its generalized forms The celebrated Kalman-Yakuboviˇc-Popov (KYP) lemma [Willems (1971); Rantzer (1996)] originates from Popov’s criterion [Popov (1962)] and the positive real lemma [Yakubovich (1962); Kalman (1963); Anderson (1967)]. It has been recognized as one of the most basic tools of system theory that establishes the equivalence between a frequency-domain inequality and existence of a Lyapunov function of certain form.

Then the following statements are equivalent. 32) hold. 32) holds even if (A, B) is not controllable. 5, where θ0 := (θ1 + θ2 )/2, γ := 2 cos θc and θc := (θ2 − θ1 )/2. 7. Let complex matrices A, B, Π, and real scalars θ1 , θ2 be given. Suppose that Π = Π∗ , (A, B) is controllable, and 0 < θ2 − θ1 ≤ 2π. Define Θ := {θ ∈ R|θ1 ≤ θ ≤ θ2 }. The following are equivalent. 35) holds. 35) holds even if (A, B) is not controllable. 5 and Schur complement the corresponding result follows for the case that G(λ) is a proper transfer matrix.

12. 16) then there exists an admissible controller K such that Tzw ∞ < γ. 17) I −C1 Pf Sf−1 0   × 0 Sf−1 0 ; −1 0 Ph 0 where Sf := Pf − Pg−1 > 0. December 14, 2008 17:15 World Scientific Book - 9in x 6in 42 ws-book9x6˙wang LMI Approach to H∞ Control In reference [Masubuchi et al. 16) is proved. One may observe that the above method is a unified approach to linear controller synthesis that employs various LMI conditions to represent control specifications. By defining a comprehensive class of LMIs, which contain the LMIs that have been conventionally used in linear control design, a convex parametrization of all controllers as well as the existence conditions can be obtained.

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Analysis And Control Of Nonlinear Systems With Stationary by Jinzhi Wang, Zhisheng Duan, Ying Yang, Lin Huang
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