On the structure at infinity of linear block-decouplable systems: The general case

Abstract

The aim of this note is to show that a linear system ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C, A, B</tex> ) is block-decouplable by means of static state feedback laws ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F, G</tex> ) with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</tex> invertible if and only if the infinite structure of ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C, A, B</tex> ) equals the union of the infinite structures of the subsystems ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C_{i}, A, B</tex> ) extracted from the given output partition. This result generalizes the ones recently obtained for Morgan's problem [6] and for the particular cases of right-invertible [7] or left-invertibie [8] systems.