In this article a Constrained Finite Time Optimal Controller (CFTOC) for Networked Controlled Systems (NCS) is presented for the case where: a) the induced network delays are uncertain and bounded, and b) there are constraints in the magnitude of the control action and the outputs/states of the system. Based on the assumption that the round-trip latency time varies within known bounds, the uncertain network-induced delays are embedded in the system model resulting in a polytopic uncertain system. A polytopic uncertain system model is developed for the cases where: a) the uncertain delay is smaller than the sampling period, and b) the delay is longer than one sampling period but can be decomposed into a fixed known part (integer multiple of the sampling period) and an uncertain part bounded by one sampling period. When the constraints on the input and the output/state are added, the control objectives can be cast in a CFTOC formulation, and the resulting affine control law guarantees both the robust stability and the robust performance of the closed loop system, while satisfying the constraints. Simulation results are presented that prove the efficacy of the proposed control scheme.