How to get the range of a complex Inequality

I am trying to get the range of values from a complex inequality that I am trying to solve. For example in the following code:

syms kp ki

a5=1;
a4=((2047986680487193847267328*ki - 13715030938073068*kp))/(2047986680487193847267328*kp + 87042659012253300578844672);
a3=(((184889681621683227480892934480434054447104*kp)/625 - 13715030938073068*ki +    17196119675118872248493326935156326400))/(2047986680487193847267328*kp + 87042659012253300578844672);
a2=(((184889681621683227480892934480434054447104*ki)/625 - (22196527874515618602308700203063*kp)/16384))/(2047986680487193847267328*kp + 87042659012253300578844672);
a1=(((18220068596449371851061970182309744452038457569574912*kp)/625 - (22196527874515618602308700203063*ki)/16384 + 846451363799069169891931531128018151619713564672))/(2047986680487193847267328*kp + 87042659012253300578844672);
a0=(18220068596449371851061970182309744452038457569574912*ki)/(1279991675304496154542080000*kp + 54401661882658312861777920000);
b1=(a4*a3-a5*a2)/a4;
b2=(a4*a1-a5*a0)/a4;
b3=(b1*a2-b2*a4)/b1;
b4=(b3*b2-b1*a0)/b3;

S=solve(a4>0,b1>0,b3>0,b4>0,a0>0,[kp,ki])

When I am running this code, it shows that it cannot find an explicit solution. However, when I have put the code inside two for loops and sweeped over a range of values for kp and ki, I get numerous values of them satisfying the inequalities.

But I want to get a more scientific solution instead of sweeping over a random range of values based on trial and error. Can you suggest me any modification that can help me run my code? Thank you in advance.

Answer 1

[Devineni Aslesha]

The range of complex inequality can be obtained by using the following syntax for ‘solve’ function.

S = solve(a0>0, [kp,ki], 'IgnoreAnalyticConstraints', true,'ReturnConditions', true);

For more information, refer the following link.

https://www.mathworks.com/matlabcentral/answers/328751-how-can-i-find-ranges-of-inequalities-using-solve-in-live-script