In　this　article,　a　collection　of　conditions　to　achieve　asymptotic　stability　of　switched　nonlinear　systems　with　guaranteed　safety　via　a　state-dependent　switching　law　are　provided,　where　the　asymptotic　stability　of　individual　subsystem　is　not　assumed.　Multiple　barrier　functions　and　multiple　Lyapunov　functions　(MLFs)　are　merged　as　a　tool　for　analyzing　the　asymptotic　stability　with　guaranteed　safety　control　problem　of　switched　nonlinear　systems.　Meanwhile,　the　state-dependent　switching　law　is　designed　to　refrain　zeno　phenomenon.　Moreover,　bilinear　sum　of　squares　methodologies　are　employed　to　construct　corresponding　MLFs　for　switched　nonlinear　systems.　Finally,　three　simulation　examples　are　introduced　to　prove　the　effectiveness　of　the　provided　method.