control theorem proofs

I'm looking for an experienced control system to help me with some control theorem proofs. The difficulty level of the work is intermediate and I have specific theorems that need to be proved using step-by-step equations and explain it . This project will require someone with deep theoretical understanding of mathematics and a good command of both written and analytical problem solving skills. I have a series of proofs to be completed and I am working to a strict deadline, so the successful freelancer will need to be able to complete the work in an efficient manner. If you have experience in tackling complex, control system problems that involve understanding mathematical concepts, analyzing and interpreting data and solving problems away from the standard textbooks, I would like to hear from you.

theorem 3 use equation (12)

theorem 4 use Remark 1 assumptionS A1 , A2