Laplace transform - Continuous and Discrete Time Signals and Systems - page 319

6.30 (a) Using the M ATLAB function roots , calculate the location of poles
and zeros of the following transfer functions:
(i) H 1 ( s ) = s 2 − 5 s − 84

s 4 + 7 s 3 − 33 s 2 − 355 s − 700 ;
(ii) H 2 ( s ) = s 2 − 19 s + 84

s 4 + 7 s 3 − 33 s 2 − 355 s − 700 ;
(iii) H 3 ( s ) = s 3 + 20 s 2 + 15 s + 61

s 4 + 5 s 3 + 31 s 2 + 125 s + 150 ;
(iv) H 4 ( s ) = s 3 − 10 s 2 + 25 s + 7

s 6 + 6 s 5 + 42 s 4 + 48 s 3 + 288 s 2 + 96 s + 544 ;
(v) H 5 ( s ) = s 2 + 3 s + 7

s 3 + (6 − j7) s 2 + (11 − j28) s + (6 − j21) .
(b) From the location of poles and zeros in the s-plane, determine if the
systems are (i) absolutely stable, (ii) marginally stable, or (iii) unstable.