Hill-Rom Holdings Inc. said Wednesday that it has agreed to buy privately held Welch Allyn Inc. for about $2.05 billion in cash and stock, adding diagnostics to the medical company’s portfolio. Chicago-based Hill-Rom provides wound care, surgical safety and respiratory health products, among other items. Welch Allyn, Skaneateles Falls, N.Y., makes medical-diagnostic equipment. The combined company will have $2.6 billion in revenue and a portfolio of diagnostics, sensing and patient monitoring technologies. Under the terms of the deal, Welch Allyn shareholders will receive about $1.6 billion in cash and about 8.1 million newly issued shares of Hill-Rom stock. After the deal closes, expected by the end of September, Welch Allyn shareholders will have a 13% stake in the combined company.