They allege the Silicon Valley firm was engaging in "deceptive, immoral, and unethical" business practices and that the software update was not a fix, as described by Apple, but a design to "purposefully slow down or 'throttle down' the performance speeds" of older phones.
According to the court filings, they claimed that "their older iPhone models slows down when new models come out".
Critics have long accused the firm of "planned obsolescence", suggesting that it used software updates to limit phone performance ahead of a new model release but there has previously been little evidence to confirm this was the case.
But on Wednesday Apple admitted that it had been limiting earlier iPhones to fix a sudden shutdown glitch.
"Our goal is to deliver the best experience for customers, which includes overall performance and prolonging the life of their devices," a spokesman said.
Older iPhone batteries struggle to supply the required maximum current needed to power the phone processor at full speed, causing it to shut down unexpectedly, Apple confirmed.
By slowing the performance, the phone does not need the maximum current, and will no longer switch off without warning.
Apple's latest software update, the iOS 11, was found to have drained some older iPhone batteries more than twice as fast as the previous system, iOS 10 did upon its launch in September this year.
Apple launched its most expensive phone in October, the iPhone X, which boasts facial recognition, a 5.8inch display and wireless charging.
Apple has been contacted for comment.
