Texas Air Corp. took formal control of Continental Airlines today, ending a lengthy, costly and bitter takeover battle that started more than a year ago when Texas International Airlines, a TAC subsidiary, began buying stock in the larger Continental.

Full control passed at Continental's annual shareholders' meeting in its home town with the approval of an 11-member board of directors selected by TAC, which holds 50.8 percent of Continental's outstanding shares. The new board includes only three holdovers from the old Continental board, including Continental President George A. Warde. TAC won the last of its needed governmental approvals for its acquisition last fall.

Today's somewhat anticlimatic meeting was in sharp contrast to last year's raucous annual meeting in Denver when hundreds of Continental employes crowded into a meeting room to cheer and applaud Continental officials who were fighting the takeover. Roy M. Rawls, Continental's senior vice president for finance, told shareholders today that Continental spent $10 million last year in fighting the takeover bid, seeking to establish an employe-owned company as an alternative, and promoting a doomed merger with Western Airlines.

In his report to shareholders, Warde said the airline's current efforts to reduce operating expenses by $100 million annually through layoffs, pay cuts and work-rule concessions could, if fully implemented, mean a "break-even" year for Continental, which has lost money in each of the last three years.

"But by fully utilizing the benefits of the relationship between the two airlines, we foresee a more dramatic . . . improvement for 1982, and beyond," he said.

Warde said that although the two airlines will operate as separate entities, they have already found "very encouraging" the benefits of "joining forces."

TAC President Frank Lorenzo, an industry innovator who began the quest for Continental with profits earned on an earlier unsuccessful attempt to buy National Airlines, told shareholders that both airlines had arrived "at deregulation's doorstep" with problems. Continental had a high-cost structure and no planes or routes to feed their long-haul routes; Texas International had lower costs but no long routes to feed from their short-haul route structure. Together, they complement each other nicely and will be "very strong together," he said. "I'm tremendously optimistic that this company will emerge as one of the great companies in a deregulated environment," he said.