       Trial and Error using mathematica.

• To: mathgroup at smc.vnet.net
• Subject: [mg30696] Trial and Error using mathematica.
• From: teee at i-kool.com (Kritchai)
• Date: Sat, 8 Sep 2001 02:22:53 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Dear sir,
Here is my problem,

M(s,a1,a2)=a1*(5.5*s+7)+a2*(s^2+0.5*s+2) / (s+1)*(s+10)

derived from Laplace Transform (s=jw that w is frequency (red./sec.)).
In this case I considered two cases: M(jw,a1=1,a2=1) and
M(jw,a1=1,a2=-1).
I want to bound the magnitude of M (i.e., |M(jw,a1=1,a2=1)| and
|M(jw,a1=1,a2=-1)|) by W(s) at each frequency. In this case the
magnitude of M is in dB (Decibel unit). Therefore, my work would be to
find a "W(s)" such that |W(jw)^-1*M(jw,a1,a2)| is less than or equal
to "one" for all w. This verified by plotting the functions in
frequency domain. The following is that I found in the text book- In
"analytical" and accurate approach we could have verified that there
were no intersections between the two curves by equating them and
computing corresponding zeros. I would like you to show me for the
algorithm to compute W(s) using MATHEMATICA.
Thank you for your kindness and I would be glad to hearing from you
soon.
Best regards,
Kritchai.

```

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