Improved results on generalised robust H ∞ filtering for Lipschitz descriptor non‐linear systems with uncertainties

Abstract

Recently, a generalised framework for robust non-linear H ∞ filtering of uncertain Lipschitz descriptor systems has been developed by Abbaszadeh and Marquez. The main feature of the associated H ∞ filter is that it holds a general structure, which can capture both dynamic and static-gain filter structures. In this study, the authors aim to propose improved results on the general H ∞ filter synthesis for Lipschitz descriptor non-linear systems in the presence of disturbance and model uncertainties. Based on a technique to directly deal with the Lipschitz non-linear terms, new H ∞ filter synthesis conditions that guarantee asymptotic stability of the estimation error dynamics with prescribed disturbance attention level are established and formulated in terms of linear matrix inequalities. They also give some remarks on the results of Abbaszadeh and Marquez and compare them with the author's results. More precisely, it is shown that the proposed conditions are less conservative than those in the existing results. Simulation results on an example are given to numerically verify the proposed design.