problemset4

problemset4 - 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 Four C. Caramanis Not Due. This problem set should serve as a start for your review for the test. It covers the concepts introduced in Chapter 5. This includes homogeneous and particular solutions to LTI systems (CT and DT); The matrix exponential; Jordan Canonical Form and linear algebra; and stability of LTI systems. Also, while it also covers some of the earlier concepts discussed, it is not exhaustive. We had a lot of practice with linearization in class and in previous problem sets, so while that is an important concept, it is not emphasized in this one. It is de±nitely important for the midterm. 1. Consider the matrix: A = 1111 2 0 30 2 8 000 2 5 0004 7 0000 6 (a) If you can, write down the Jordan Canonical Form (JCF) of this matrix and explain which results you are using in order to arrive to your answer. If you cannot, explain why there is ambiguity. (b) Is the system ˙ x = Ax stable, unstable, or stable i.s.L., for A the above matrix? (c) Is the system x [ k +1]= Ax [ k ] stable, unstable, or stable i.s.L., for A the above matrix?

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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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problemset4 - The University of Texas at Austin Department...

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