WASHINGTON — Converse Inc. and Ralph Lauren Corp. have entered into a settlement agreement and filed a joint motion to terminate a trademark infringement case involving footwear pending before the U.S. International Trade Commission, according to ITC documents.

Converse, owned by Nike Inc., filed a complaint in October against 32 retailers and manufacturers alleging they infringed on some of the brand’s trademarks used in certain shoes. The ITC initiated an investigation against the companies in November.

In addition to Ralph Lauren, the ITC complaint named companies such as Wal-Mart Inc., Kmart Corp., H&M, Skechers, Fila, Iconix Brand Group, Aldo Group and Tory Burch.

Converse claimed in the complaint that all of the defendants have infringed on its iconic midsole trademark design made up of a toe bumper and a toe cap, plus either an upper stripe and/or lower stripe, associated with its “All Star” high-top sneakers that were first introduced in 1917 and renamed “Chuck Taylor” after a Converse salesman and basketball player.

In a redacted version of the settlement agreement on the ITC Web site, Ralph Lauren agreed to destroy its entire inventory of products named in the ITC complaint within 30 days of the agreement going into effect, including component parts, tools and molds, advertising, promotional materials and packaging.

Several Ralph Lauren shoe styles — 36 in total — were cited as infringing on Converse’s trademarks in the settlement agreement, including washed canvas, Western leather, camouflage shoes and bleached denim shoes.

The company also agreed to cease and desist from manufacturing, advertising, promoting, selling, distributing, importing or exporting the accused products as long as Converse’s midsole trademark remains valid and enforceable.

Ralph Lauren will also make a payment to Converse, although the amount was redacted from the public version of the settlement agreement.