Saudi Arabia has taken another big step toward building the most modern air defense system in the Persian Gulf region with the award of $1.1 billion in contracts for installation of an elaborate ground network that will hook into five warning and control system aircraft slated to patrol the skies round the clock.

In announcing the awards to the Boeing Co. this week, the Defense Department said the contracts represent an implementation of a commitment made in 1981 and do not violate the Reagan administration ban earlier this year on new arms sales to the Middle East.

The Saudis have a long list of weapons, including fighter planes, that they want to buy besides the new air defense system, according to administration officials.

Israel has objected in the past to the buildup of the Saudi air force. The Carter and Reagan administrations have taken the position that it is in the U.S. interest to help Saudi Arabia protect its oil fields.

Fighter planes and the five AWACS (airborne warning and control system) aircraft that the Saudis have agreed to buy, four for round-the-clock surveillance and the fifth as a spare, can be used defensively or offensively.

The 17 radars Boeing will install in Saudi Arabia are designed to detect aircraft flying at low or high altitude and will be deployed to cover all the country's air approaches.

The Air Force Electronics System Division evaluated bids from Hughes Aircraft Co. and Litton Systems Inc. before awarding the contracts to Boeing, the Air Force said.

The air defense system will be built to allow later expansion.