By Dragoslav D. Siljak

ISBN-10: 0126434301

ISBN-13: 9780126434309

Starting with a graph-theoretic framework for structural modeling of complicated structures, the textual content offers effects regarding strong stabilization through decentralized kingdom suggestions. next chapters discover optimization, output suggestions, the manipulative strength of graphs, overlapping decompositions and the underlying inclusion precept, and reliability layout. Notes and references complement every one bankruptcy, and the appendix presents a precious diversity of effective graph algorithms.

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We first claim that B has some fixed zero rows. Otherwise, for any p, = pi such that cp(p:, b ) $ 0, since p(A* - X I ) 2 n - 1 for all X # 0, we can choose a % = p; such that cp(p:, p i ) # 0 and p([A* - X I B*])2 n for all X # 0, contradicting the assumption. 107) A21 A22 + where &is ni x ni, a = 1, 2, with n1 n2 = n, and B 2 has no fixed zero rows. If A12 = 0 , the proof follows. Suppose A 1 2 # 0. 6. I -, X,I < n1, ~121) for some x 47 VA11A12, # 0. 108) If ,422 is nondegenerate, since B 2 contains no zero rows, p A z l ,pAZ2and can be fixed such that p ([A;,- XI B;])2 n2 for all X # 0, so that again A ~ ~ .

This assumption is made for two distinct reasons. First, physical plants are made up of parts and by identifying individual parts, or groups of parts, as subsystems, we can take advantage of the structural features of the system in a control design. Second, we may ignore the physical boundaries of components and decompose a large system into “mathematical” subsystems which have no obvious physical identity. This type of decomposition can bring about a considerable savings in computer memory and time when systems of high dimensions are involved.

69) where Bc = 0 and Cc = 0. 36 belong to this class of models. With the notion of a decentralized plant firmly in place, we are ready to formulate the decentralized constraints on feedback control laws. 1) can be altered efficiently by feedback without changing the plant itself. ,Kailath, 1980). 70) where the constant output gain matrix K = ( k i j ) has dimension m x i! and feedback coefficients kij. 70) to S , we obtain the closed-loop system S: X = (A - BKC)s. 5. 1) an index set Ji = {j : where M = (1, 2, trollers of the form rcij .

### Decentralized Control of Complex Systems by Dragoslav D. Siljak

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