I cannot state the Lipschitz nonlinear system is beneficial just because the LMI is available. Need to find some merits from the system application etc.
Have a look at::: http://www.shuyouyu.com/publication/proceeding/22Tube%20MPC%20scheme%20based%20on%20robust%20control%20invariant%20set%20with%20application%20to%20Lipschitz%20nonlinear%20systems.pdf
There exists a bundle of literature in which researchers have been examined/concluded that most of the real world data have very complex structure that may not directly lie in linear vector spaces (linear models produces low computational/modeling/recognition accuracy), that is why it has been assumed that the real world complex structured data (e.g., images, videos, text, etc...) may lie in nonlinear spaces (in practice modelling via considering nonlinear spaces produces better accuracy ). This is the main reason due to which researchers prefer nonlinear model frameworks.