Feedback invariants via output injection
Two input-state systems are called feedback equivalent if there exists a basis transformation on the state space, a basis transformation on the input space, and a feedback which (together) transform the first system into the second one. The class of feedback equivalent input-state systems is characterized by the invariant factors and the minimal indices of the associated pencil. Here, the authors study the following problem: given a class of feedback equivalent input-state systems and the quadruple \((A,B,C,D)\), when does there exists an output injection \(K\) such that \((A+KC, B+KD)\) becomes an element of the equivalence class. This problem has a long history, see, e.g., \textit{I. Cabral, F. Silva} and \textit{I. Zaballa} [Linear Algebra Appl. 332--334, 447--458 (2001; Zbl 1049.93038)]. The novelty of this paper is that the underlying field is arbitrary, and thus may be finite.
scientific article; zbMATH DE number 2083523
scientific article