  We present a comprehensive theory of the Dyakonov-Shur (DS) plasma
instability in current-biased graphene transistors. Using the hydrodynamic
approach, we derive equations describing the DS instability in the
two-dimensional electron fluid in graphene at arbitrary values of electron
drift velocity. These nonlinear equations together with Maxwell's equations are
used for numerical analysis of the spatial and temporal evolution of the
graphene electron system after the DS instability is triggered by random
current fluctuations. We analyze conditions necessary for the onset of the DS
instability and the properties of the final stationary state of the graphene
electron system. We demonstrate that the instability results in the coherent
anharmonic oscillatory state of the electron fluid and calculate both the
spatial distribution and the power of the electromagnetic radiation generated
by the graphene transistor in the DS instability regime.
