In this paper, we investigate the process of detection of False Data Injection (FDI) in a Linear Parameter Varying (LPV) cyber-physical system (CPS). We design a model based FDI detector capable of detecting false data injections on output measurements and scheduling variables. To improve the detection accuracy of FDI attacks, the attack detector design uses the performance metric H_ to maximize the detection capability of the detector module to effectively detect FDI attacks. On the other hand, it uses the metric to minimize the effect of disturbance on the detector module given an unreliable network. We assume that the network unreliability comes from packet dropout that we modeled as Bernoulli process. The FDI attack detector is designed such that H_ and performance metrics are maintained despite packet dropout. Based on stochastic stability, we define a set of sufficient Linear Matrix Inequalities (LMI) that we solve as a multi-objective optimization problem to obtain the detector gain. The obtained detector gain is used for estimating the current system state and current output measurement using the system input, manipulated measurements and manipulated scheduling variables. Then, the output of the detector is compared with the actual sensor measurement. The resulting residual signal carries the information about the FDI attack.The proposed approach is tested and validated on a two-tank system. The evaluation results demonstrate that the proposed detector is able to detect FDI attacks.