Optimal control of discrete-time interval type-2 fuzzy-model-based systems with D-stability constraint and control saturation

This paper investigates the optimal control problem for discrete-time interval type-2 (IT2) fuzzy systems with pole constraints. An IT2 fuzzy controller is characterized by two predefined functions, and the membership functions and the premise rules of the IT2 fuzzy controller can be chosen freely. The pole assignment is considered, which is constrained in a presented disk region. Based on Lyapunov stability theory, sufficient conditions of asymptotic stability with an H ∞ performance are obtained for the discrete-time IT2 fuzzy model based (FMB) system. Based on the criterion, the desired IT2 state-feedback controller is designed to guarantee that the closed-loop system is asymptotically stable with a prescribed H ∞ performance condition and all the poles rest in the disk region. Finally, two numerical examples are shown to illustrate the effectiveness of the presented design scheme. HighlightsAn IT2 fuzzy control system and an IT2 fuzzy controller of discrete-time are first constructed in this work.It is not required that the discrete-time IT2 fuzzy control systems and fuzzy controller share the common lower membership functions and common upper membership functions, the membership functions and the premise rules of the IT2 fuzzy controller can be chosen freely.The IT2 fuzzy state-feedback controller with an input constraint is designed for the discrete time IT2 FMB control systems, which ensures that all the poles of the closed-loop system are rested in a given disk region.

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