H_inf and mu-synthesis controlers could be same?

In my project, I created Hinf and mu-synthesized controllers. And as a result, I got the same controller systems, can something like this happen?

Answer 1

[Divit]

Hi Orhan Koray ÇALIK,

I understand that you are using H_inf and mu-synthesis controller systems and you got the same controller system from the two different approaches.

Yes, it is possible to obtain the same controller systems when using H_inf and mu-synthesis techniques. Both H_inf control and mu-synthesis are robust control techniques that aim to design controllers that provide robust performance and stability guarantees in the presence of uncertainties and disturbances. Moreover mu-synthesis extends the methods of H_inf synthesis to design a robust controller.

Although the design methodologies and mathematical formulations of H_inf control and mu-synthesis are different, they share some similarities in terms of the underlying principles and objectives. Both techniques involve optimizing a cost function subject to certain constraints to achieve robust stability and performance.

I recommend you refer the following documentation links to know more about the same:

• https://in.mathworks.com/help/robust/ref/uss.musyn.html
• https://in.mathworks.com/help/robust/controller-synthesis.html
• https://in.mathworks.com/help/robust/mu-synthesis.html

I hope the answer addresses your queries.