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

Constitutes the 1st CASY workshop on Advances up to speed thought and functions which used to be held at collage of Bologna on could 22-26, 2006. This name comprises chosen contributions through the various invited audio system and comprises clean leads to regulate. it truly is compatible for engineers, researchers, and scholars up to the mark engineering.

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8) By substituting the expression of α in the above expression we obtain (36). 2 K Symmetric and Circulant The stability result proposed in the previous section is not the best one can ﬁnd. Indeed, consider a strongly connected circulant undirected graph G (V, W), where V and W are respectively the set of vertices and the set of arcs, and where |V | = N . Assume that the in-degree of the graph is ν + 1. We associate to the graph G (V, W) the matrix K ⎧ 1 if i = j and i → j ⎨ ν+1 ν if i = j Kij = − ν+1 ⎩ 0 otherwise 46 R.

The main objective of the present paper is to understand whether it is possible to design some smart encoding/decoding strategies such that a control law of the form (5) yields the consensus for the overall system. In the sequel we concentrate our attention on a particular way of exchanging information which ﬁts into the previous scheme: the logarithmic quantized strategy. 4 Logarithmic Quantizers This strategy is based on the techniques proposed in [17]. In this case we assume the following form for equation (8) 36 R.

This implies that x(t) → v T x(0)1. In the special case when v = N −1 1 we obtain that the consensus is achieved at the average of the initial conditions. In this case I + K is said to be a doubly stochastic matrix and K a average consensus controller. We observe that the use of control law as in Equation (3) implies the exchange of perfect information through the communication network. More precisely, the fact that the element in position i, j of the matrix K is diﬀerent from zero, means that the system i needs to know exactly the state of the system j in order to compute its feedback action.