The　present　study　is　concerned　with　the　fault　detection　for　a　class　of　switched　systems　with　dwell-time　constraint　in　discrete-time　domain.　Different　from　the　reported　results,　the　considered　disturbances　and　faults　are　relaxed　to　the　case　with　bounded　magnitude　rather　than　the　bounded　energy.　To　address　this　situation,　the　dwell-time　dependent　∞　fault　detector　is　then　constructed　for　implementing　detection　process.　More　incisively,　when　the　magnitude　is　known　in　advance,　a　reachable-based　fault　detector　is　also　designed　to　improve　the　detection　performance.　In　addition,　with　the　dwell-time　dependent　Lyapunov　function　approach,　several　sufficient　conditions　for　the　existence　of　the　∞　and　reachable-based　fault　detectors　are　derived,　and　a　practical　example　is　provided　to　demonstrate　the　applicability　of　the　proposed　detection　methods.　©　2022　IEEE.