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a) Draw the pole-spread of the polynomial. b) Find the Routh table of the polynomial and examine the stability. c) Calculate Hurwitz matrices and the corresponding determinants. Examine the stability of the polynomial family using the 4th Hurwitz determinant.

a) Draw the pole-spread of the polynomial. b) Find the Routh table of the polynomial and examine the stability. c) Calculate Hurwitz matrices and the corresponding determinants. Examine the stability of the polynomial family using the 4th Hurwitz determinant.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider an uncertain polynomial given as follows: 288s 173q1s³ 262853 2091915² P(s, q) = s5+q₁s4 + + ·+945³ + + 11 19 11 14 5935 37945 9379s 14645q1 592 793 1994 8143 + + 10 15 3 9 7 +935² + 63945²10026s² + 25 11 where the uncertain parameters are bounded as 0 ≤ qi≤ 100 (for i=1,2,3,4). 6193q1s 8 +9₂s + a) Draw the pole-spread of the polynomial. b) Find the Routh table of the polynomial and examine the stability. c) Calculate Hurwitz matrices and the corresponding determinants. Examine the stability of the polynomial family using the 4th Hurwitz determinant. d) For q2=100, q3= q4= 0, examine the stability of the polynomial by the help of Bialas Theorem.
Transcribed Image Text:Consider an uncertain polynomial given as follows: 288s 173q1s³ 262853 2091915² P(s, q) = s5+q₁s4 + + ·+945³ + + 11 19 11 14 5935 37945 9379s 14645q1 592 793 1994 8143 + + 10 15 3 9 7 +935² + 63945²10026s² + 25 11 where the uncertain parameters are bounded as 0 ≤ qi≤ 100 (for i=1,2,3,4). 6193q1s 8 +9₂s + a) Draw the pole-spread of the polynomial. b) Find the Routh table of the polynomial and examine the stability. c) Calculate Hurwitz matrices and the corresponding determinants. Examine the stability of the polynomial family using the 4th Hurwitz determinant. d) For q2=100, q3= q4= 0, examine the stability of the polynomial by the help of Bialas Theorem.
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