A delay-dependent approach to robust generalized H₂ filtering for uncertain continuous-time systems with interval delay

This paper is interested in the problem of robust generalized H₂ (GH₂) filtering for uncertain continuous-time systems with a delay in the state and polytopic uncertainty in system matrices. The delay is assumed to vary in an interval with a nonzero lower bound. Based on a new LyapunovKrasovskii functional (LKF), by virtue of free-weighting matrix method and the projection lemma, a new sufficient condition for analyzing the robust GH₂ performance of the filtering error system is first derived, and then by employing a simple linearization procedure, a new design method is proposed in terms of a set of linear matrix inequalities. Since no useful term is neglected in estimating the upper bound of the derivative of the LKF and the lower bound of the delay is included in the obtained conditions, the results in the paper are much less conservative than the open ones, which is finally illustrated by a numerical example.