Digital control of nonlinear systems is studied by output feedback. It is proved that for nonlinear systems with a lower triangular structure, semiglobal asymptotic stabilization is still possible via discretized output feedback as long as a sampling time is small. The establishment of semiglobal asymptotic stabilizability needs no restrictive condition on the nonlinearities and/or unmeasurable states of the system, such as a linear growth condition or an output-dependent growth condition as commonly required in the case of global output feedback stabilization. It involves, however, tedious but subtle stability analysis due to the hybrid nature of the closed-loop system. A design method through "sample and hold" is developed to construct a semiglobally asymptotically stabilizing, digital output feedback compensator that consists of a high-gain nonlinear observer and controller, both with saturated states.