problemset5

# problemset5 - 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 Five C. Caramanis Due: Wednesday, October 21, 2009. This problem set focuses on the new concepts introduced in the last two classes: reachability and state feedback. As usual, we also work in some exercise with important concepts from linear algebra. 1. Reachable Canonical Form: Consider the system from above: A = - 14 3 26 - 1 - 2 - 52 ,B = 0 0 1 (a) What is the reachable canonical form, ˜ A , for the matrix A ? (b) In class we showed that ˜ A and A are related by the relationship: ˜ A = TAT 1 ,forsome invertible matrix T . 1 We showed in class that this kind of transformation preserves eigenvalues, and therefore also determinants. Use Matlab (you can compute by hand, if you wish) to verify that ˜ A and A havethesamee igenva lues ,andthesamedeterm inant (equal to the product of the eigenvalues). (c) Follow the procedure we outlined in class (and also outlined in the text) to compute the invertible matrix T that can be used to transform from A to ˜

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## This note was uploaded on 10/26/2009 for the course EE 362K taught by Professor Friedrich during the Fall '08 term at University of Texas at Austin.

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problemset5 - The University of Texas at Austin Department...

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