Question: How to find the condition on variables such that the expression is positive?

Hi all,

I have the following expression,

Typesetting[delayDotProduct](b, K[P], true)+k*K[D]-(Typesetting[delayDotProduct](b, m[1], true)+Typesetting[delayDotProduct](b, m[2], true)+K[D]*m[2])*k*K[P]/(Typesetting[delayDotProduct](b, K[D], true)+k*m[1]+k*m[2]+K[P]*m[2]-m[1]*m[2]*(Typesetting[delayDotProduct](b, K[P], true)+k*K[D])/(Typesetting[delayDotProduct](b, m[1], true)+Typesetting[delayDotProduct](b, m[2], true)+K[D]*m[2]))

where K and K_P are the controller gains, k is the stiffness, b is the damper, m1 and m2 are masses.

How can I find the condition on variables such that the numerator of this expression is greater that zero?

The conditions should appear as inequalities.


 

b*K[P]+k*K[D]-(b*m[1]+b*m[2]+K[D]*m[2])*k*K[P]/(b*K[D]+k*m[1]+k*m[2]+K[P]*m[2]-m[1]*m[2]*(b*K[P]+k*K[D])/(b*m[1]+b*m[2]+K[D]*m[2]))

b*K[P]+k*K[D]-(b*m[1]+b*m[2]+K[D]*m[2])*k*K[P]/(b*K[D]+k*m[1]+k*m[2]+K[P]*m[2]-m[1]*m[2]*(b*K[P]+k*K[D])/(b*m[1]+b*m[2]+K[D]*m[2]))

(1)

``


 

Download Routh-Hurwitz_stability.mw

 

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