Explicit solvability conditions for the general discrete-time H∞ almost disturbance decoupling problem with internal stability

Abstract

We present in this paper several sets of numerically checkable solvability conditions for the discrete-time H∞ almost disturbance decoupling problem with internal stability and with either (i) full information feedback, or (ii) full state feedback, or (iii) general measurement feedback. The problem considered here is general in the sense that we allow the subsystems of a given system to have invariant zeros on the unit circle. More importantly, our conditions are to be explicitly expressed in terms of some well-defined geometric subspaces, and, furthermore, these conditions can easily be verified numerically. © 1999 Taylor & Francis Ltd.