Motivated　by　switched　service　systems　with　multiple　buffers　controlled　by　a　single　server　to　educe　multiple　output　flows　simultaneously,　the　paper　introduces　a　special　class　of　linear　hybrid　automata.　It　is　proved　that　the　linear　hybrid　automata　can　be　reduced　to　a　linear　discrete-time　system　with　periodic　coefficients.　Moreover　it　is　shown　that　the　linear　hybrid　automata　admits　a　periodic　trajectory,　and　the　theorem　for　asymptotic　stability　of　the　periodic　trajectory　are　given.　Finally,　our　result　is　applied　to　prove　stability　of　the　switched　server　system.　©　2011　IEEE.