This paper investigates the design of an unknown input interval observer, for linear parameter varying systems. The proposed method provides a solution to the decoupling conditions under L-2-gain and L-infinity-gain performance level. It is shown that the design of the unknown input interval observer parameters can be formulated as a SDP problem. The major advantages with regard to other solutions is that first, it does not require the explicit knowledge of a (time-varying) state transformation, for the estimation error dynamics to satisfy the Meztler property. Rather, it is shown how such a property can be formulated as a part of the SDP optimization process; Second, decoupling and L-2/L-infinity constraints are formulated on the thickness of the interval length in spite of half the interval length. The proposed methodology is illustrated on a numerical academic example. (C) 2019 Elsevier Ltd. All rights reserved.