Based　on　Delta　operator,　in　which　the　sampling　period　is　an　explicit　variable,　a　unified　design　method　of　non-fragile　guaranteed-cost　speed　controller　for　permanent　magnet　linear　synchronous　motor　(PMLSM)　under　different　sampling　period　is　studied.　The　condition　of　existence　of　the　controller　is　given　in　LMI　form.　In　the　pole　analysis　of　the　PMLSM,　we　find　that　even　if　the　parameters　of　the　PMLSM　and　the　controller　are　subject　to　additive　norm-bounded　variations,　the　closed-loop　system　is　still　asymptotically　stable,　and　the　upper　bound　of　the　mathematical　expectation　of　the　cost　function　can　be　obtained　as　well.　However,　the　closed-loop　system　will　be　unstable　if　the　controller　gain　variations　are　not　considered.