Robust H<inf>2</inf> filtering for discrete LTI systems with linear fractional representation

Abstract

This paper introduces a new approach to H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> robust filtering design for discrete LTI systems subjected to linear fractional parameter uncertainty representation. We calculate a performance certificate in terms of the gap between the lower and the upper bounds of a minimax programming problem, which defines the optimal robust filter and the associated equilibrium cost. The calculations are performed through convex programming methods, applying slack variables, known as multipliers, to handle the fractional dependence of the plant transfer function with respect to the parameter uncertainty. The theory is illustrated by means of an example borrowed from the literature and a practical application involving the design of a robust filter for the load voltage estimation on a transmission line with a stub feeding an unknown resistive load.