Stability analysis of linear linguistic control systems

This paper presents numerical procedure of linear linguistic control systems(LLCSs) and their stabilities using IT2 fuzzy approach. Firstly, When multiple uncertain property of information is considered, interval type-2 fuzzy sets (IT2FSs) are rightly employed to be basic variables in the LLCSs. Consequently, linear conventional control systems (LCCSs) are abstracted into their linguistic counterparts. Secondly, their numerical procedure can be obtained by IT2 fuzzy decomposition theorem. Thirdly, their stabilities are also investigated. Existence of stable linguistic state vector (LSV) and stability condition is discussed in detail. Finally, properties of LLCSs are compared with those of LCCSs by several numerical examples, which confirms that it is correct that our proposing LLCSs and their stabilities.