This review devotes its major attention to analyzing the physical processes that govern the stability of uniform burning of the volume gas discharges that are used to excite high-pressure CO$_2$ lasers. An analysis is given of the theoretical and experimental studies that have shown a substantial increase in the time of uniform burning of a non-self-sustaining gas discharge as the electric power density is decreased. Specificially, this has made it possible to convert the discharge in practice into a steady-state burning regime at elevated gas pressure. The optical characteristics of gas mixtures based on carbon dioxide that are established upon excitation of the medium by a steady-state non-self-sustaining discharge are examined.