Solvability and one side invertibility for implicit descriptions

The authors consider (E,A,B,C) systems described by Σ:Ex=Ax+Bu and y=Cx which are either left or right invertible. The aim is to propose a natural left or right inverse for this system which will be given in a similar (E,A,B,C) description. It is proven that Σ^a (the proposed inverse) is an actual one-side inverse if Σ is solvable and one-side invertible. A short example is given