Find the parameter that satisfies the condition

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mir 2023-9-10

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https://ww2.mathworks.cn/matlabcentral/answers/2019021-find-the-parameter-that-satisfies-the-condition

编辑： Bruno Luong 2023-9-10

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Hi everyone, let me explain my problem better.

For example

syms j w lambda

a = ((1 - 3*j*w)*(1 + 5*lambda*j*w))/((14 + j*w)*(2 + lambda*j*w)^3)

a =

Q = subs(a,j,sqrt(-1))

Q =

I = subs((1 + 2*j*w)/(0.5 + j*w),j,sqrt(-1))

I =

I need to find the real lambda value that satisfies the following condition:

abs(Q)<abs(I)

ans =

I tried with a for loop incrementing the value of lambda from time to time, but I got the following error:

'Conversion to logical from sym is not possible.'

Is there a more efficient solution that can solve my problem?

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Bruno Luong 2023-9-10

I haven't specified what is w or where it varies

mir 2023-9-10

编辑：mir 2023-9-10

@Bruno Luong

It's the pulsation.

The condition must be valid for every value of w

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Answer 1

Bruno Luong 2023-9-10

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https://ww2.mathworks.cn/matlabcentral/answers/2019021-find-the-parameter-that-satisfies-the-condition#answer_1306231

编辑：Bruno Luong 2023-9-10

There is not solution

where w goes to i/2 (the rhs goes to inf) or -i/3 (the lhs goes to 0), for any lambda the inequality won't be satisfied.

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mir 2023-9-10

@Bruno Luong ok thanks, but I wasn't looking for the solution to the condition, it was just an example.

I'm looking for a method to deal with symbolic inequalities in multiple variables and solve them with respect to a defined variable, in this case lambda.

Bruno Luong 2023-9-10

编辑：Bruno Luong 2023-9-10

Well this question shows what you expect to solve does not have solution.

What you compare is absolute value of two polynomials (considered as variable in w) and coeffs depend on lambda:

|P(w)| <= Q(w)|

The fundamental theorem of algebra tells Q(w) always have a root (w) somewhere in the complex plane. So in general you cannot find a solution lambda that do what you want since the inequality is false at the root of Q.

Sorry there is no symbolic trick and the symbolic engine cannot (yet?) does this kind of (simple) math inference.

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