Delay‐dependent robust ℋ ∞ filter design for state‐delayed discrete‐time linear systems via homogeneous polynomial matrices

This study presents new robust linear matrix inequality (LMI) conditions for robust ℋ ∞ full‐order filter design of discrete‐time linear systems affected by time‐invariant uncertainty and a time‐varying state delay. Thanks to the use of a larger number of slack variables, the proposed robust LMI conditions contain and generalise other results from the literature. LMI relaxations based on homogeneous polynomial matrices of arbitrary degree are used to determine the state‐space realisation of the full‐order filter, that can also be implemented with delayed state terms whenever the time‐delay is available in real time. As another contribution, an iterative LMI‐based procedure involving the decision variables is proposed to improve the ℋ ∞ filter performance. Numerical experiments illustrate the better performance of the proposed filter when compared to other approaches available in the literature.