Output feedback H∞$$ {H}_{\infty } $$ control of linear systems with infinite distributed input delays

Abstract

This article investigates the output feedback control problem of linear systems with infinite distributed input delays. An observer‐based output feedback (OBOF) controller is proposed via the predictor feedback approach, and a sufficient condition for the existence of the OBOF controller is given in terms of a set of linear matrix inequalities. It is shown that the resulting closed‐loop system is globally exponentially stable with a prescribed performance. The obtained results include some results on the same problem for linear systems with bounded distributed input delays as special cases. Two numerical examples are finally presented to illustrate the effectiveness of the proposed controller.