His second wife, Frances, was also named in Tuesday's lawsuit, which claimed she contributed to a hostile work environment and failed to stop Robinson's alleged sexual misconduct.
The women are suing under the pseudonyms Jane Doe 1, 2, 3 and 4, due to the sexual misconduct allegations, including rape, being levelled against the musician.
In the 27-page lawsuit they detail several incidents dating back to 2006 and allege they were pressured into sex.
All four women, who are of Hispanic descent, said they had not come forward until now because they feared losing their livelihood, familial reprisal or embarrassment. Some were concerned the allegations could affect their immigration status.
They are seeking at least $50m in damages and a jury trial.
No police reports or criminal charges have been filed against the musician.
The women's lawyers held a press conference on Tuesday, accusing Robinson of being a "serial and sick rapist" who "must be stopped".
This drew the ire of the Robinson's legal team, who called it a "bizarre" attempt "to enlist the public as an unwitting participant in the media circus they are trying to create".
"We will have more to say in the coming days as we make our legal response, and in time Mr Robinson will respond in his own words," Mr Frost said.
"We ask anyone following this case to reserve judgment as the evidence comes to light and all the actual facts of the case unfold.
"We will be asking the Court to dismiss the lawsuit. We will also be asking the Court to address that in their statements to the press about Mr Robinson, the plaintiff's attorneys have reached beyond the bounds of liberties that even lawyers are typically allowed in this context."