Celtic Design Spiral Patterns by Aidan Meehan

By Aidan Meehan

The oldest and such a lot regularly Celtic kind of layout, spiral styles illustrate vividly the continuity among pagan and Christian Celtic artwork. Spirals are a continuing presence, from the artwork of overdue Stone Age valuable Europe, via megalithic temple sculptures, the los angeles Tene bronzes of the Gauls and Britons, and Pictish jewels, to the original procedure of layout constructed in Celtic arts golden age within the early center a long time. Aidan Meehan supplies specific functional suggestion on the right way to adapt that residing culture to the calls for of mnrlern craft and layout.

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BITMEAD To do this, choose m' > η — min rank(^4 — pil) + 1. Since i rank[exp(,4T) - exp(p t T)7] = rank(^4 - ptI) Eq. (128) implies that Eq. (130) holds for almost all m x m' constant matrices Go- In addition, from rankG > η — min rank(A — pi I) i it is easy to see that for an arbitrary constant matrix Go and Vz GC rank rank e x p ( ^ T ) - zl C exp(^T) - z l C 0 DGo + w! > 2n — min rank(yl — ptI) -f 1 i / 0 > 2n — min rank(;4 — pt I) Thus, our appeal to Lemma 7 in [13] shows that Eq. (131) generically holds n x m mxm with respect to ( G , G 0 ) G J K ' xIR ', from which the theorem follows.

A N D E R S O N , W E I - Y O N G Y A N , A N D R O B E R T R. 209 ki8 5 . 07 ki J 3 4 8 . 49 J 8 6 . 385 Then C(z) stabilizes kP(z) for each fe G [fei, * 2 ] - On the other hand, one of the GSHF gains associated with G0 and G by Eqs. 408], F(t)= 0 < * < 1/8 1/8 < t < 3/16 3 / 1 6 < * < 1/4 Thus, the GSHF compensator stabilizing kP(s) for each fe G [fei, k2] can be constructed as Zk + l — . 245 - 0 . 0 2 5 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 = u(t) = 0 [Ci C2 F(t)vk, c3 CA C*5 for t £ [kT, •ί- - 0 .

Control 27, pp. 885-903 (1978). 8. B. A. Francis and T. T. Georgiou, "Stability Theory for Linear TimeInvariant Plants with Periodic Digital Controllers," IEEE Trans. Autom. Control AC-33, pp. 820-832 (1988). 9. P. Khargonekar, K. Poolla, and A. Tannenbaum, "Robust Control of Linear Time-Invariant Plants Using Periodic Compensation," IEEE Trans. Autom. Control AC-30, pp. 1088-1096 (1985). 10. P. T. Kabamba, "Control of Linear Systems Using Generalized Sampled-Data Hold Functions," IEEE Trans. Autom.

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