This　paper　provides　some　sufficient　conditions　to　achieve　asymptotic　stability　of　switched　systems　under　spatio-temporal　specifications　via　a　state-dependent　switching　law.　A　common　finite-time　barrier　function,　multiple　barrier　functions　and　multiple　Lyapunov　functions　are　merged　as　a　tool　for　analyzing　the　asymptotic　stability　of　a　switched　nonlinear　system　under　spatio-temporal　specifications.　Finally,　a　numerical　example　is　presented　to　demonstrate　the　effectiveness　of　our　proposed　method.　©　2021　Technical　Committee　on　Control　Theory,　Chinese　Association　of　Automation.