A. Implicit DescriptionsIn this section, we recall some basic facts about the stability and stability of implicit descriptions. We refer the reader, for example, to [5], [14] for more details. The qualitative behavior of (1) strongly depends on the structure of the matrix pencil E − A, ∈ C. For ease of notation, let us write (E,A) := E − A. Definition 1: An implicit description (1) is called regular system if the pencil (E,A) is regular, that is to say if| E-A| 6≡0. (2)In other words, a pencil (E,A) is regular if there exists such that | E-A| 6= 0. The regularity of (E,A) is important since it guarantees that, for any admissible input, the solutions of (1) exist and are unique. Hypothesis 1: The pencil (E,A) is regular. The determinant in (2) can be written as | E-A| = k n1 i=1( − i) , where n1 ≤ n (n1 = n if and only if E is not singular) and k is a real constant. We refer to (E,A) = { 1, 2, . . . , n1} as finite eigenvalues ​​of the pencil (E,A)2. By an appropriate change of base, a regular system can always be decomposed into the so-called Weierstrass form x˙ 1(t) = Jx1(...