Abstract
This paper is interested in the problem of robust generalized
H
2 (G
H
2) 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 Lyapunov–Krasovskii functional (LKF), by virtue of free-weighting matrix method and the projection lemma, a new sufficient condition for analyzing the robust G
H
2 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.
► The model is more general than zero lower bound case considered in the literature. ► Less conservative analysis conditions for G
H
2 filters have been proposed. ► Less conservative design for G
H
2 filters has been proposed.