We consider the problem of stabilizing a linear time-invariant system in the presence of sporadic output measurements and intermittent access to the plant input. The plant is equipped with a zero-order hold device which stores the value of the input between transmissions. We propose an observer-based controller composed consisting of a measurement-triggered observer which experiences jumps in its state whenever a new measure is available, a state-feedback control law computed from the estimated state, and a copy of the zero-order hold device feeding the plant, which jumps whenever the control input is transmitted to the plant. The closed-loop system is modeled as a hybrid system that includes two timers triggering the two different events. The resulting hybrid system is analyzed as the cascade of hybrid systems and its asymptotic stability properties are established through a separation principle. In addition, an efficient design procedure is presented and illustrated in an example.