# lecture10 - 10.RouthHurwitzCriterion

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1 10.  Routh-Hurwitz Criterion Solving the characteristic equation for roots is  DIFFICULT. Question: Can we conclude stability without solving  the characteristic equation? Answer: Yes, use the Routh-Hurwitz Criterion It will tell if the characteristic equation has unstable  poles or not. Furthermore, if it is unstable, it will also tell how many. This involves constructing an array and observe the  sign changes in the first column.

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2 Routh-Hurwitz Array Let the characteristic equation be         a 1 s n +a 2 s n-1  +a 3 s n-2  +a 4 s n-3  +…+a n s+a n+1  = 0 We form the array: s n : a 1 a 3 a 5 s n-1  : a 2 a 4 a 6 Then we construct the s n-2  row as follows:  s n : a 1 a 3 a 5 s n-1  : a 2 a 4 a 6 s n-2  : b 1 b 2 where ... etc. a a a a a b ; a a a a a b 2 6 2 5 1 2 2 4 2 3 1 1 - = - =
3 Routh-Hurwitz Array (cont.) Then we construct the s

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## This note was uploaded on 11/09/2009 for the course ENG 91301 taught by Professor Lui during the Spring '08 term at Hong Kong Institute of Vocational Education.

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lecture10 - 10.RouthHurwitzCriterion

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