Reduced-order ℒ ₂ –ℒ _∞ filtering for singular systems: a linear matrix inequality approach

Abstract

The reduced-order ℒ2–ℒ∞ filtering problem for singular systems is investigated. The objective is to design a filter with the order less than the original system, such that the resulting error systems are regular, impulse-free and stable while the close-loop transfer function from the disturbance to the filtering error output satisfies a prescribed ℒ2–ℒ∞ norm-bound constraint. First the linear matrix inequalities (LMIs) conditions of ℒ2–ℒ∞ performance for singular systems are given. Then, the necessary and sufficient conditions are obtained in terms of LMIs coupling with non-convex rank constraint. An explicit parameterisation of all desired reduced-order filters is presented. Specifically, the full-order and the static filtering result in convex LMI conditions and a simple parameterisation of all the desired filters is also given. It is shown that the presented results can be considered as extension of existing results on ℒ2–ℒ∞ filtering for state-space systems. Finally, a numerical example is provided to demonstrate the effectiveness of the presented approach.