SUCCEEDING A COMPANY'S FOUNDER IS NEVER easy. That’s what Abhi Talwalkar did when he joined LSI Corp. as president, CEO and director in May 2005. Milpitas, California–­based electronics pioneer LSI had fallen on hard times, and long-standing investors were clamoring for a fix.

Wilfred Corrigan, the British-born engineer who had run Fair­child Camera and Instrument Corp. — considered the birthplace of Silicon Valley — launched the business as LSI Logic in 1981 with $6 million in venture capital. At the time, major U.S. and Japanese corporations ruled the electronics industry. LSI Logic focused on customized silicon chips, a niche market; by the late 1980s it dominated the business. Early in the next decade, it began offering systems and design tools too. Between 1998 and 2003, LSI acquired a dozen companies and broadened its product lines as the semiconductor business contracted. When revenue plunged in 2003, the company cut costs and jobs.

To put LSI back on its feet, the board replaced Corrigan with Talwalkar, then co–general manager of Intel Corp.’s digital enterprise group, which included the semiconductor giant’s corporate client, server, storage and communications businesses.

Talwalkar inherited a company that had expanded into everything from networking to consumer goods, including video-processing chips that went into DVD players and the Sony PlayStation video game console. With so many products, it was no longer on the leading edge of anything. But Talwalkar foresaw that people would increasingly use smartphones and other mobile devices to do things like post to Facebook and watch movies.....