New results on robust H ∞ filtering design for discrete-time piecewise linear delay systems

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Original languageEnglish
Pages (from-to)183-194
Journal / PublicationInternational Journal of Control
Issue number1
Publication statusPublished - Jan 2009


This paper revisits the problem of robust H filtering design for a class of discrete-time piecewise linear state-delayed systems. The state delay is assumed to be time-varying and of an interval-like type, which means that both the lower and upper bounds of the time-varying delay are available. The parameter uncertainties are assumed to have a structured linear fractional form. Based on a novel delay-dependent piecewise Lyapunov-Krasovskii functional combined with Finsler's Lemma, a new delay-dependent sufficient condition for robust H performance analysis is first derived and then the filter synthesis is developed. It is shown that by using a new linearisation technique, a unified framework can be developed so that both the full-order and reduced-order filters can be obtained by solving a set of linear matrix inequalities (LMIs), which are numerically efficient with commercially available software. Finally, a numerical example is provided to illustrate the effectiveness and less conservatism of the proposed approach.

Research Area(s)

  • Delay-dependent, Linear fractional uncertainty, Linear matrix inequalities, Piecewise linear delay systems, Robust filtering