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Test if F(S)=2S6+4S5+6S4+8S3+6S2+4S+2 is a Hurwitz polynomial.

written 3.5 years ago by teamques10 ★ 67k

•   modified 3.5 years ago

control systems

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written 3.5 years ago by teamques10 ★ 67k

Consider ROUTH-ARRAY METHOD

$s^6$	2	6	6	2
$s^5 $	4	8	4	-
$s^4$	$ =2 | {(4*6)-(2*4)}/4 =4 | {(4*2)-(2*0)}/4 =2 | - | | $s^3$ | {(2*8)-(4*4)}/2 =0 ---\gt(8) | {(2*4)-(2*4)}/2=0---\gt(8) | 0 | ...R1 | | $s^2$ | {(4*8)-(2*8)}/8 =2 | {(2*8)-(0*2)}/8 =2 | - | - | | $s^1$ | {(8*2)-(2*8)}/2= 0---\gt(4) | 0 | - | ...R2 | | $s^0$ | {(4*2)-(2*0)}/4= 2 | - | - | ...R3 | * From the row of$s^3$ ,we can observe that the coefficients of these terms are becoming zero. Thus, to avoid this we write an auxillary equation from the row of $s^4$ as follows $A(s)=2s^4+4s^2+2$  and its derivative is $A'(s)=8s^3+8s$ Thus replacing the row of $s^3$ by coefficients of above derivatives * From the row of$s^1$,we can observe that the coefficients of these terms are becoming zero. Thus, to avoid this we write an auxillary equation from the row of $s^2$as follows   $B(s)=2s^2+2$and its derivative is  $B'(s)=4s$

Thus replacing the row of by coefficients of above derivatives

• From the first column of the above table we can observe that all the coefficients of F(s) are positive.

Hence given polynmial is a HURWITZ POLYNOMIAL.

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