Oblique detonation wave (ODW) stabilized over a ramp or a wedge can be used for combustion in a supersonic combustion chamber. This paper numerically studies the conditions for an ODW to be stabilized over a finite ramp length at different temperature, pressure and Mach number conditions, and examines potential combustor control methods in order to achieve desirable ODW combustor characteristics for a propulsion system. At given operating conditions, ramp length and for a given amount of heat release, attached ODWs can only be stabilized over a certain range of ramp angles. Furthermore, for fixed combustor geometry the ODW induction length can be larger than the available ramp length. Also, either the ODW inclination angle can be too low for complete combustion of the entire inflow mixture or the ODW can impinge on the upper combustor wall when the ODW angle is too large. Both these conditions can have detrimental effects on the combustor performance. The effects of changing the combustor flow properties on the formation of ramp-supported ODWs are examined, in order to analyze the possible methods to obtain desirable combustor characteristics. The possibility of varying the ramp angle for combustor characteristic control is also analyzed. The effects of temperature, pressure and equivalence ratio variations on the ODW induction length and angle, as well as the effects of varying the ramp angle, are analyzed and compared. Results indicate that a coupled combustor characteristic control technique is possible, relying for the most part on variations of physical flow properties and partly on slight variations of the ramp angle.