The lawsuit is the latest shot in the battle for control between Dauman and Shari Redstone, who is vice chair of both Viacom and CBS, and president and a director at National Amusements.
On Friday, Sumner Redstone removed both Dauman and Abrams from the trust and from the board of directors of National Amusements. He expressed concerns to them about Viacom's performance and received no response, according to a statement by Redstone's attorney, Michael Tu, on Saturday.
Viacom said in a statement its board has tried to meet with Sumner Redstone many times, adding that he was silent during a recent call about the company's strategy, including its planned sale of a stake in movie studio Paramount.
The Sumner M. Redstone National Amusements Inc Trust owns about 80 percent of Redstone's privately held National Amusements, which in turn owns 80 percent of the voting stock in both Viacom and CBS.
Besides Shari, trust members include Shari Redstone's son, lawyer Tyler Korff; David Andelman, another lawyer who is on the CBS board; Norman Jacobs, Sumner Redstone's divorce lawyer; and Leonard Lewin, an attorney who represented Redstone's first wife, Phyllis, in her divorce from Redstone.
After Sumner Redstone is incapacitated or dies, the trust would determine all matters that come to a shareholder vote at both companies, including potential mergers or acquisitions.
Viacom, like other media companies, has suffered from falling ratings at its cable networks as younger viewers migrate to online and mobile video.
Sumner Redstone is planning to name National Amusements Inc general counsel Tad Jankowski and family friend Jill Krutick to the seven-person trust, sources told Reuters on Sunday.
Viacom shares rose 3 percent, climbing above $40 a share on Monday. Over the past 12 months, the stock is down 40 percent, lagging the Standard & Poor's 500 Media Index, which is off 4.7 percent.