Robust filtering for uncertain two‐dimensional continuous‐discrete state‐delay systems in finite frequency domains

Abstract

In this work, the problem of robust H ∞ filtering for uncertain two-dimensional (2D) continuous-discrete Roesser systems with state delays in finite frequency ranges is investigated. This study first develops the equivalence between a frequency domain inequality (FDI) and a linear matrix inequality. In particular, the proposed result covers FDIs in finite frequency intervals for 2D continuous/discrete/continuous-discrete settings. Using the result, the existing finite frequency bounded ream lemmas and the finite frequency positive real lemmas have been generalised to uncertain 2D state-delay Roesser systems. Then, a robust finite frequency H ∞ filter design method for uncertain 2D continuous-discrete state delay Roesser systems is given. Finally, examples are provided to clearly demonstrate the effectiveness of the proposed method.