The present paper provides novel and comprehensive parameter-dependent filter designs based on the Luenberger structure for a general class of discrete-time linear parameter-varying (LPV) systems modeled via linear fractional representations (LFR). The main contributions rely on using \(\mathscr{H}_{2}\) and induced ℓ2 performance criteria, including a mixed approach, to obtain the synthesis of Luenberger-type filters in terms of LMI-based conditions. The novel conditions can also handle LPV systems efficiently with rational and nonlinear dependence of the time-varying parameters through slack variables. The proposed synthesis conditions are expressed by taking parameter-dependent Lyapunov (PDL) functions combined with static full-block multipliers into account, addressing three different approaches for the filter structure. Moreover, the formulation also deals with bounded rates of parameter variation, such that the filter synthesis results can be more comprehensive and less conservative. The effectiveness of the proposed LPV/LFR filter designs is validated by means of numerical examples considering both \(\mathscr{H}_{2}\) and ℓ2 performances, as well as the rate of parameter variation.
