Non-minimal order low-frequency H∞ filtering for uncertain discrete-time systems

Abstract

This paper proposes a sufficient condition for the discrete-time robust H∞ filtering design problem with low-frequency specifications using an extension of the generalized Kalman-Yakubovich-Popov lemma. The matrices of the system are supposed to be uncertain, time-invariant and to belong to a polytopic domain. The proposed approach takes advantage of a non-minimal filter structure, that is, a filter with order greater than the order of the system being filtered, to provide improved H∞ bounds for low-frequency specifications. The condition can be solved by means of linear matrix inequality relaxations with slack variables and Lyapunov matrices which are considered as homogeneous polynomials of arbitrary degree. Numerical examples illustrate the improvements on the H∞ bounds provided by the non-minimal filter structure in combination with the more accurate polynomial approximations (higher degrees) for the optimization variables.