Robust energy-to-peak filter design for a class of unstable polytopic systems with a macroeconomic application

Abstract

This paper deals with the robust energy-to-peak filtering problem for linear continuous- and discrete-time systems with polytopic uncertainties. Motivated by a macroeconomic application, the notion of the robust energy-to-peak filter is extended to a class of unstable systems by making use of the results on stability with respect to noncompact sets. Parameter-dependent Lyapunov approach and Finsler’s lemma are used to establish sufficient conditions for the existence of energy-to-peak filter such that the error system is asymptotically stable with respect to a subspace and a prescribed energy-to-peak performance is guaranteed. The conditions are formulated in terms of linear matrix inequalities (LMIs). Two numerical examples modified from the literature are provided to demonstrate the effectiveness of the proposed method. The results are also successfully applied to the estimation of the so called potential GDP using real data.