Download Chain-scattering approach to h[infinity] control by Hidenori Kimura PDF

By Hidenori Kimura

1 Introduction.- 2 parts of Linear structures Theory.- three Norms and Factorizations.- four Chain-Scattering Representations of the Plant.- five J-Lossless Conjugation and Interpolation.- 6 J-Lossless Factorizations.- 7 H-infinity regulate through (J, J')-Lossless Factorization.- eight State-Space strategies to H-infinity keep watch over Problems.- nine constitution of H-infinity regulate

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We need some further definitions. DEFINITION 22. Let ( A ; A , v ) , ( B ; A , v ) be weak partial lattices, q : A --c B. W e call q a homomorphism iff whenever m b exists for a, b E A , then aqAbq exists and (aAb)q= ayAbpl,,and the similar condition holds for v. A one-to-one homomorphism q is a n embedding provided that ar\b exists iff aqwbq exakts, and the similar condition holds for v . If g~ is onto and q is a n embedding, then q is a n isomorphism. Now we are ready again to define the most general lattices of Section 2.

To prepare for them we prove : re, LEMMA 16. Let (H; A , v ) be a weak partial lattice. ” If avb exists, then avb =sup {a, b}. I f aAb exists, then aAb =inf {a, b}. Also, a

I,,-l. By Definition 1, a polynomial is just a sequence of symbols. , .. DEFINITION2. A n n-ary polynomial p defines a function inn variables (a polynomial function, or simply, a polynomial) on a lattice L by the following rules (ao,. ,a,,- E L ): (i) I f p = x i , p ( a o an-,)=ai,O

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