Terahertz frequency time-domain spectroscopy employing free-space radiation has frequently been used to probe the elementary excitations of low-dimensional systems. The diffraction limit, however, prevents its use for the in-plane study of individual laterally-defined nanostructures. Here, we demonstrate a planar terahertz frequency plasmonic circuit in which photoconductive material is monolithically integrated with a two-dimensional electron system. Plasmons with a broad spectral range (up to ~ 400 GHz) are excited by injecting picosecond-duration pulses, generated and detected by a photoconductive semiconductor, into a high mobility two-dimensional electron system. Using voltage modulation of a Schottky gate overlying the two-dimensional electron system, we form a tuneable plasmonic cavity, and observe electrostatic manipulation of the plasmon resonances. Our technique offers a direct route to access the picosecond dynamics of confined electron transport in a broad range of lateral nanostructures.