Ali,

In general, most stability analysis that apply to nonlinear systems and their control apply to linear systems as well. The reverse is not always true.

So something like Lyapunov Stability Criterion or Popov Stability Criterion, both of which essentially apply to nonlinear systems, should be applicable to the hybrid (linear + nonlinear) systems that you have in mind.

Selection of the stability functions may become more involved, but the techniques themselves should work !

Cheers !

-Sanjay

Dear Sanjoy Roy,

Thanks a lot for your useful answer.

Regards

Ali

Dear Ali,

Indeed it would be more rigorous this agree on the word hybrid (linear + nonlinear) as was noted Prof. Sanjoy or switched and hybrid so in this case we will use Multiple Lyapunov Function. I propose a rather interesting paper attached.

Best regards

Dear Prof  Mohamed,

Thanks a lot it really useful references. 

Regards,

Ali