This work concerns the design of a multi-objective unified qLPV observer for the state estimation problem in LPV systems with a parameter-dependent control input matrix. The standard forms of the system and the observer are first presented, where the observer matrices are functions of the estimated states (qLPV problem). The effects of bounded unknown input disturbances are decoupled from the estimation error thanks to the parameterization of the observer matrices. To treat the disturbance caused by inexact scheduling parameters, we introduce an upper bound on the parameter estimation error, which is considered uncertainty. Then, the effects of the control input and the random measurement noise on the estimation error are minimized using the H∞ and generalized H2 conditions, respectively, as a multi-objective optimization problem. In the solution of the LMI sets, the projection lemma is applied to reduce the high conservativeness that would otherwise lead to suboptimal results. Then this observer is applied to a semi-active automotive suspension system written in LPV form, using simulations with real data measured from our experiment test platform, and compared with the linear time-invariant H∞ and H2 observers.