A brief and some further insight on the Exact Quadratization of nonlinear control systems

This paper aims to be, first of all, a short survey on the topic of the Exact Quadratization (EQ) of nonlinear control systems, mainly related to our article on the same subject recently issued (2015) in the SIAM Jou. on Cont. & Opt.. Secondly, it aims to yield some additional material, further improvements and new insights, not present or not enough discussed in the main ??-systems, and a detailed description of the relationship between solutions of the original and quadratized representations.