What authority does a court have to disqualify an attorney?

A trial court's authority to disqualify an attorney comes from its inherent power to "control in furtherance of justice, the conduct of its ministerial officers, and of all other persons in any manner connected with a judicial proceeding before it, in every matter pertaining thereto." (Code Civ. Proc., 128, subd. (a)(5); People ex rel. Dept. of Corporations v. SpeeDee Oil Change Systems, Inc. (1999) 20 Cal.4th 1135, 1145, 980 P.2d 371 (SpeeDee Oil).) By virtue of this authority, the trial court has discretion to disqualify or not disqualify an attorney.