Eleven persons injured in bloody clashes between demonstrators during the state visit of the shah of Iran here Nov. 15-16 filed a $19 million lawsuit yesterday, alleging their civil rights were violated by anti-shah demonstrators and that police failed to provide adequate protection.

THe claimants - ranging from a 9-year-old boy who was reportedly beaten in the head, arms and legs to a Chicago bricklayer who says he was stabbed in the leg by a knife - have asked for a variety of compensatory, punitive and property damages totaling $19,403,500.

The lawsuit stems primarily from a Nov. 15 clash on the Ellipse near the White House when hundreds of stickwielding anti-shah Iranian students attacked a gathering of several thousand pro-shah demonstrators during the ceremonial arrival of Shah Mohammad Reza Pahlavi at the White House.

At least 96 demonstrators and 28 U.S. Park Police officers were injured, some seriously, in the most violent outbreak here in several years. Police, overwhelmed by the attacking students, fired tear gas and reinforcements arrived to help disperse the crowd. More demonstrations and a few hit-and-run skirmishes between pro-and anti-shah factions continued that day and into the next.

Some Park Police officers complained later they were ill-prepared for the violence and that available D.C. police were not called in to help. FBI and State Department officials also said police planners apparently ignored early warnings of a likely clash between the hostile Iranian factions.

Yesterday's lawsuit, filed in U.S. District Court here, was leveled against both D.C. and Park Police as well as several anti-shah demonstration leaders and organizations, including the Iranian Student Association in the United States, the Muslim Youth Organization and the Organization of Iranian Moslem Students.

The plaintiffs include several Assyrian-Americans and other Iranian ethnics from Chicago who had come to Washington in an elaborately organized effort to offset the militant anti-shah students.

One other plaintiff is Robert Ita, a Nigerian who according to attorney Albert Rapoport, was a bystander at the Ellipse. He was beaten by students, Rapoport said, when he attempted to prevent the students from clubbing a woman.

Student organizers, who acknowledge their followers include a variety of Marxists and non-Communist socialists, blame the violence variously on Iranian secret police provocateurs and random anarchist elements in their ranks.

The Iranian Embassy here was denied involvement in organizing the pro-shah demonstrations or sending in secret police (SAVAK).