Abstract: We investigate the optimal-estimation and state-feedback-controller design problems of networked control systems using the stochastic event-driven communication protocol. Based on the random communication mechanism of the actuators/sensors and controller, we modeled the network-based system as a Markov jump system. Using this framework, we designed an optimal state estimator based on the time-varying Kalman filter theory. Then, based on Markov-jump-system and dynamic programming theories, we derived an optimal controller satisfying the quadratic cost function that guarantees the stability of networked systems containing partial observations. Finally, we provide a numerical example to demonstrate the feasibility and effectiveness of the proposed method.