Decoupling by restricted static-state feedback: The general case

Abstract

In this paper we tackle the general block decoupling problem, for linear constant dynamical systems ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C, A, B</tex> ) with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</tex> inputs and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> outputs, with restricted static-state feedback, in other words with control laws of type <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u = GFx + Gv</tex> . We give a necessary and sufficient condition of existence for such laws which generalizes the one previously given in [2] for the simple case <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k = p \leq m</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> denotes the number of blocks to be decoupled.