This　paper　studies　model　predictive　control　(MPC)　with　control　barrier　function　to　solve　the　stability　and　safety　problems　of　switched　systems　subject　to　input　and　state　constraints.　Considering　that　the　system　state　is　unmeasurable　and　disturbed,　an　observer-based　MPC　$　H_\infty　$　H　infinity　method　is　adopted　to　estimate　the　system　state　and　suppress　disturbances.　A　cost　function　is　designed　to　optimise　the　state　and　control　input　of　switched　systems　by　minimising　its　upper　bound,　and　the　optimisation　problem　is　further　transformed　into　a　feasibility　problem.　Moreover,　a　control　barrier　function　is　introduced　to　constrain　the　controller　gains,　which　ensures　that　the　initial　state　of　switched　systems　converges　to　the　steady　state　without　entering　the　specified　unsafe　region.　Furthermore,　a　set　of　matrix　inequality　conditions　is　given　to　express　the　input　and　state　constraints.　Then,　the　Lyapunov　function　and　average　dwell　time　(ADT)　approach　are　used　to　obtain　sufficient　conditions　for　the　asymptotic　stability　of　switched　systems.　Finally,　two　simulation　examples　are　given　to　verify　the　effectiveness　of　the　proposed　method.