Energy-to-peak filtering for singular systems: the discrete-time case

Both full-order and reduced-order energy-to-peak filtering problem for discrete-time singular systems are investigated. The purpose is to design a filter with desired order, such that the resulting error systems are regular, casual and stable while the closed-loop transfer function from the noises to the filtering error output satisfies a prescribed /(2) - /(infinity) norm bound constraint. First, based on some augment technique, the generalised bounded real lemma with guaranteed energy-to-peak performance for discrete-time singular systems is derived. Then, the necessary and sufficient conditions for the solvability of the energy-to-peak filter are obtained in terms of linear matrix inequalities (LMIs) coupling with a non-convex rank constraint. An explicit parameterisation of all desired energy-to-peak filters is presented. When the full-order or the static filtering is considered, convex LMI conditions and a simple parameterisation of all the desired filters are also given. Furthermore, the presented results are shown to cover the existing results on energy-to-peak filtering for regular state-space systems.