Assignment #21 ECSE-2410 Signals & Systems - Spring 2009 Due Fri 04/17/09 1(30). Use the Routh array as discussed in class to determine the number of roots that the following polynomials have in the right half of the s-plane, if any. Note that (c) requires the special case of the Routh array where a 0 is replaced by a small positive number ε . Use the roots command in Matlab to check your answers. (a) s 4 + s 3 + 2s 2 + 5s + 8 (b) s 5 + s 4 + 2s 3 + s + 5 (c) s 5 + 2s 4 + 2s 3 + 4s 2 + 11s + 10 2(10). For the polynomial. , use the Routh array to determine the range of () K s s s s s p + + + + = 2 3 2 3 4 such that all roots have negative real parts. Use Matlab to verify your bounding (between right 0> K and left half planes) value of K i.e., substitute your bounding K into Matlab roots and show that the resulting roots of contain a pair of () s p axis j − ω roots and two real roots that have negative real parts. 3(30).
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