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 structures with desk bound units are very important simply because they disguise loads of functional platforms in engineering. past research has been in keeping with the frequency-domain for this type of platforms. besides the fact that, few effects on robustness research and controller layout for those structures are simply to be had.
This booklet provides the research in addition to tools in keeping with 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 basically single-input and single-output platforms. The regulate tools provided during this e-book could be precious for study on nonlinear platforms with desk bound units.
Contents: Linear structures and Linear Matrix Inequalities; LMI method of H keep watch over; research and keep watch over of optimistic genuine 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 keep an eye on for doubtful suggestions Nonlinear platforms; keep watch over of Periodic Oscillations in Nonlinear platforms; Interconnected platforms; 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
The statements are equivalent: (i) A is stable and C(sI − A)−1 B + D ∞ < γ; (ii) there exists a symmetric matrix P > 0 such that T A PA − P AT P B CT B T P A B T P B − γ 2 I DT < 0. 6 ws-book9x6˙wang LMI Approach to H∞ Control Small gain theorem The small gain theorem is an important result for stability test of a nominally stable system under unstructured uncertainties. Essentially, it states that if a feedback loop consists of stable systems and the loop gain product is less than unity, then the feedback loop is internally stable.
I=1 December 14, 2008 17:15 World Scientific Book - 9in x 6in 16 ws-book9x6˙wang Linear Systems and Linear Matrix Inequalities Obviously, if the condition (II) holds, then the condition (I) holds. But the converse is not true. Similar to the case of non-strict inequalities, the equivalence between the condition (I) and (II) for p = 1 can also be found in [Yakubovich (1971, 1973a, 1977); Fradkov and Yakubovich (1979); Huang (2003)]. The corresponding result can be summarized as follows. 2. Assume that there exists some x0 such that xT0 F1 x0 > 0.
A bisection algorithm is presented by Boyd and Balakrishnan [Boyd et al. (1989)] and Robel [Robel (1989)], to compute the RL∞ norm with graranteed accuracy, using the relation between the singular values of the transfer function matrix and the eigenvalues of a related Hamiltonian matrix as follows (a) select an upper bound γu and a lower bound γl such that γu ≤ G ∞ ≤ γl ; (b) if (γu − γl )/γl ≤specified level, stop; G ∞ ≈ (γu + γl )/2, otherwise go to the next step; (c) set γ = (γu + γl )/2; (d) test if G ∞ < γ by calculating the eigenvalues of H for the given γ: if H has an eigenvalue on jR, set γl = γ; otherwise set γu = γ; go back to step (b).