Dear Alireza Hosseinnajad

I have a little knowledge from homogeneous controllers, without any insight on the densely mathematical proofs associated to analyses and synthesis of these controllers. However, fortunately, I can cite a paper for you to refer, for an idea on the answer to your question. I have attached a screenshot of the paper for your perusal. In the plot attached, you see the linear and switched (probably a sliding mode controller), are less efficient in control signal convergence trend. I mean the control signal versus time converges faster by homogeneous controller than either the sliding mode controller or linear controller. The plot is in logarithmic scale, however, in real-scale it similarly could be damped versus time, faster than the other two alternatives.

The paper is cited as:

Article On Homogeneous Finite-Time Control for Linear Evolution Equa...

I have attached the PDF to my comment.

Dear Saeb AmirAhmadi Chomachar

Thanks for your recommendation of the article which has considered the design in details. It provided me with a new insight into the homogeneous controllers.

Dear Alireza Hosseinnajad

You are most welcome. Hope you be successful in your research.

There is another paper, which in the sense of mathematical formalism, seems less abstract than the paper I cited in my previous comment. I suggest you to have a look on the paper cited here as:

https://ieeexplore.ieee.org/document/609245

Finite-time stability of homogeneous systems

By: Sanjay P. Bhat and Dennis S. Bernstein

I have attached the paper in PDF format, here with my comment.

dear Saeb AmirAhmadi Chomachar

thanks for your kind help and recommendations.

I have seen similar research articles about homogeneous finite time controllers, but I am looking for something which compared the two methods and mentioned the advantages and disadvantage of homogeneous methods over finite time sliding mode controllers.

best wishes

Dear Alireza Hosseinnajad

You are welcome. In my opinion, I think such papers have not yet been contributed, because the topic is brand-new and needs more research contributions to be recently developed as some papers have been composed in 2018, 2019 and so on. You may be the one who contributes the first paper on this field and with respect to the finite-time stabilization, compare such controllers together, in terms of advantages and disadvantages.

Regards