Steve Bronson, chief executive of Qualstar Inc., has purchased more than 85,000 shares of the company’s stock in the last two weeks, pushing up his stake to more than 21 percent of outstanding shares, according to a filing with the Securities and Exchange Commission on Friday.

The Simi Valley company, which makes tape storage equipment and power supplies for computer systems, was the subject of a takeover battle last year between previous management and Bronson, the company’s second-largest shareholder. In June, shareholders voted in a new board and put in Bronson as chief executive.

Bronson holds most of the shares through Boca Raton, Fla. investment firm BKF Capital Group Inc., a publicly traded investment firm he controls. He holds a few shares through BA Value Investors LLC, another company he controls.

Together, the companies own more than 2.6 million shares of Qualstar.

Shares closed up 3 cents, or 3 percent, to $1.20 in trading on the Nasdaq.