If you sign an incriminating statement while under the influence of a controlled substance, can this be used against you in court?

If you were mentally incompetent at that time--not merely under the influence, but essentially completely unable to appreciate what you were doing, understand its consequences, etc.--then it may be the case that you can get the statement thrown out, and it's worthwhile discussing the issue with a criminal defense attorney. (If you don't have a defense attorney yet, get one NOW, and don't  speak to anyone until you do--remember, you have a right to silence. If you can't afford an attorney, one must be appointed or provided for you upon request.)

Note that the courts are hostile to the idea of letting people off or restricting the evidence against them because of a claim that alcohal or illegal drugs diminished their capacity--in those cases, if you voluntarily took the substances (it wasn't a trick; you weren't forced to take them; etc.), courts usually hold that since you voluntarily put yourself under the influence, you cannot use that to escape the consequences, including any statements you made. Also, if courts allowed this as a defense or way to invalidate statements, every perpetrator would drink, smoke, or shoot up before being arrested. It's worth exploring with an attorney, but be prepared that there is a very good chance that, unless there are exceptional circumstances, the statement will be allowed.