${\mathcal H}_{\infty }$ Functional Filtering for Linear Systems With Unknown Inputs

Abstract

A new method for ${\mathcal H}_{\infty }$ functional filtering for systems with unknown inputs is presented. First, a functional filtering technique is presented, then we show that the dynamic of estimation error can be modeled in the descriptor system form, this formulation makes it possible to describe the dynamic estimation error free of the derivative of the disturbances. The filter parameters are obtained from the bounded real lemma of descriptor systems. The developed approach unifies the design of functional, reduced-order, and full-order filters. Necessary and sufficient conditions for the solvability of the problem are obtained in terms of a set of bilinear matrix inequalities. Under certain conditions these inequalities can be transformed to a set of linear matrix inequalities. Two numerical examples are presented to illustrate the approach described in this article, the first example concerns the estimation of the state of charge of the lithium-ion battery and the second example highlights the reduced nature of the proposed functional filter.