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Exam 3 cheat sheet

# Exam 3 cheat sheet - Consider Dz= a0z5 a1z4 a2z3 a3z2 a4z...

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Consider = + + + + + Dz a0z5 a1z4 a2z3 a3z2 a4z a5 with a 0 > 0 If a 0 < 0, we consider – D ( z ), and if – D ( z ) is Schur, so is D ( z ). We form the table below. The 1 st row is the coefficients of D ( z ) arranged in descending powers of z . The second row is the reverse of the first row. We compute k 1 = a 5 / a 0 . We then subtract from the first row the product of the second row and k 1 to yield the first b i row. We then reverse the first b i row and make that the 2 nd b i row, and calculate k 2 = b 4 / b 0 , and subtract from the first b i row the product of the second b i row and k 2 to obtain the first c i row. Continue until we obtain f 0 . The Jury Test: The polynomial of degree five with a position leading coefficient in D ( z ) is Schur iff the five leading coefficients { b 0 , c 0 , d 0 , e 0 , f 0 } in the Jury Table are all positive. If any one of them is zero or negative, then the polynomial is not Schur. If the denominator of a transfer function H ( z ) is Schur, then H ( z ) is stable. The Jury Table a 0 a 1 a 2 a 3 a 4 a 5 a 5 a 4 a 3 a 2 a 1 a 0 k 1 = a 5 / a 0 b 0 b 1 b 2 b 3 b 4 0 b 4 b 3 b 2 b 1 b 0 k 2 = b 4 / b 0 c 0 c 1 c 2 c 3 0 c 3 c 2 c 1 c 0 k 3 = c 3 / c 0 d 0 d 1 d 2 0 d 2 d 1 d 0 k 4 = d 2 / d 0 e 0 e 1 0 e 1 e 0 k5 = e 1 / e 0 f 0 A polynomial is defined to be CT stable if all its roots have negative real parts. We discuss a method of checking whether or not a polynomial is CT stable without computing its roots. We use the following D ( s ) to illustrate the procedure: = + + + + + + > Ds a0s6 a1s5 a2s4 a3s3 a4s2 a5s a6 with a0 0 If a 0 < 0, we apply the procedure to -

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Exam 3 cheat sheet - Consider Dz= a0z5 a1z4 a2z3 a3z2 a4z...

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