A new approach to handle additive and multiplicative uncertainties in the measurement for LPV filtering

This paper presents a general framework to cope with full-order H∞${\mathcal {H}}_{\infty }$ linear parameter-varying (LPV) filter design subject to inexactly measured parameters. The main novelty is the ability of handling additive and multiplicative uncertainties in the measurements, for both continuous and discrete-time LPV systems, in a unified approach. By conveniently modelling scheduling parameters and uncertainties affecting the measurements, the H∞${\mathcal {H}}_{\infty }$ filter design problem can be expressed in terms of robust matrix inequalities that become linear when two scalar parameters are fixed. Therefore, the proposed conditions can be efficiently solved through linear matrix inequality relaxations based on polynomial solutions. Numerical examples are presented to illustrate the improved efficiency of the proposed approach when compared to other methods and, more important, its capability to deal with scenarios where the available strategies in the literature cannot be used.