problemset2

# problemset2 - The University of Texas at Austin Department...

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The University of Texas at Austin Department of Electrical and Computer Engineering EE362K: Introduction to Automatic Control—Fall 2009 Problem Set Three C. Caramanis Due: Monday, September 21, 2009. This problem set is intended to get us started thinking about linear algebra, and also to continue giving us some practice with Matlab. 1. Consider the matrices: A 1 = 1 - 2 - 2 4 , A 2 = 1 3 2 2 1 2 0 0 0 . Compute the Range and NullSpace of both matrices. Draw the Range of the two matrices. 2. Recall in class we discussed the consensus problem in sensor networks. This is also described in the book in Example 2.12, page 58 of the printed edition. The nodes can only see and communicate with neighbors within some distance from them. Once we draw edges repre- senting who can communicate with whom, the resulting structure is a graph: nodes joined by bi-directional edges. How quickly the estimates at the nodes converge to the true aver- age depends on graph properties of the connectivity network. This exercise explores this by looking at a few simple cases.

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