Design of the delay-dependent ℒ2-gain filters for a general class of LPV time-delayed systems

In this paper, we address the problem of designing parameter-dependent H^∞ filters for output estimation in an LPV plant that includes known state delay. We assume that state-space data depend on parameters that are not known a priori but are measurable in real-time. We investigate the required conditions to satisfy both asymptotic stability and H^∞ performance in terms of linear matrix inequalities (LMIs). The designed filters are looked for being capable of tracking the desired plant outputs in the presence of external disturbances. Two sets of LMI formulation are presented: one for a family of memoryless filters and another one for a class of filters which include state-delay in their dynamics. A simulation-based comparison is also provided in order to show the competence of our design methodology and superiority of the delayed filters relative to the memoryless ones.