By Claudio Bonivento, Alberto Isidori, Lorenzo Marconi, Carlo Rossi

Constitutes the 1st CASY workshop on Advances up to speed thought and purposes which used to be held at college of Bologna on may possibly 22-26, 2006. This name involves chosen contributions via a few of the invited audio system and includes clean leads to keep an eye on. it's appropriate for engineers, researchers, and scholars up to the mark engineering.

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Fax J A, Murray R M (2004) Information ﬂow and cooperative control of vehicle formations, IEEE Transactions on Automatic Control, 49: 1465–1476 3. Olfati-Saber R, Murray R M (2004) Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control, 49: 1520–1533 4. Olfati-Saber R (2005) Distributed Kalman ﬁlter with embedded consensus ﬁlters, Proceedings of 44th IEEE Conference on Decision and Control-European Control Conference, 8179–8184 5.

Let K be the matrix deﬁned above. Let for any δ¯2 = >0 8 . ν +1 (36) Then for any δ ≤ δ2 we have consensus, namely limt→+∞ e(t) = 0, and ∞ limt→+∞ x(t) = γ1, ∀ x(0) ∈ RN and ∀ {A(t)}t=0 . Proof. e. if i = j and i → j if i = j otherwise Finally let T = L. It is easy to verify that, letting A = I − K then B = 1 (A − I) −A + 1+ν I , D = 2+ν ν I − A and T = (ν + 1)(I − A). e. F −1 HF = diag {λ0 (H), . . , λN −1 (H)} , where {λ0 (H), . . , λN −1 (H)} is the set of eigenvalues of the matrix R. Then the condition (32) can be rewritten as α ¯ = max 0, = max λ2i (I − A) λ2i (1/(ν + 1)I − A) 1≤i≤N −1 (ν + 1)λ2i (I − A)λi (I + A) ⎧ ⎫ 1 ⎨ λ2i ν+1 I −A ⎬ max 1≤i≤N −1 ⎩ (ν + 1)λi (I + A) ⎭ By noticing that σ {A} ⊆ −1 + and σ 1 I −A ν +1 2 ,1 , ν +1 ⊆ − ν ν , .

Ir ) is said to be the initial (resp. terminal) vertex of the path. A cycle is a path in which the initial and the terminal vertices coincide. A vertex i is said to be connected to a vertex j if there exists a path with initial vertex i and terminal vertex j. A directed graph is said to be connected if, given any pair of vertices i and j, either i is connected to j or j is connected to i. A directed graph is said to be strongly connected if, given any pair of vertices i and j, i is connected to j.