H∞ LPV filtering for discrete-time linear systems subject to additive and multiplicative uncertainties in the measurement

Abstract—This paper is concerned with the problem of H∞ linear parameter-varying (LPV) filter design for discrete-time linear systems where the measurement of the scheduling parameters may be affected by additive and multiplicative uncertainties. By conveniently modeling the uncertainties and the timevarying parameters, new robust linear matrix inequality (LMI) conditions for the existence of a full order LPV filter assuring a prescribed H∞ performance, irrespective of the uncertainties affecting the measures, are given. The design procedure can simultaneously handle time-invariant uncertainties and arbitrary time-varying parameters as well. The problem is solved through LMI relaxations based on homogeneous polynomial matrices of arbitrary degree. A numerical experiment illustrates the performance of the proposed LPV filter when compared to other filters obtained with methods from the literature.