First-order linear linguistic control system and its stability

This paper presents a calculation method of first-order linear linguistic control system and its stability theorem. Firstly, in order to effectively describe information uncertainty, a first-order conventional linear control system is converted to a first-order linear linguistic control system with interval type-2 fuzzy set replacing number as basic calculation unit. Then the first-order linear linguistic control system are studied by fuzzy decomposition principle. The numerical procedure of first-order linear linguistic control system can be obtained by iterative equations of linguistic variable (interval type-2 fuzzy set) lower membership function and upper membership function α cut set endpoints. At the same time, the concepts of zero-input and zero-state responses also are proposed in the paper. Finally the stability condition of first-order linear linguistic control system is analyzed by interval type-2 fuzzy representation theorem and fuzzy decomposition principle. The effectiveness of the proposing algorithms is evaluated by a few numerical examples.