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

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 time-varying 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.