Dissipativity‐Based Controller Design for Time‐Delayed T‐S Fuzzy Switched Distributed Parameter Systems

Abstract

This paper studies fuzzy controller design problem for a class of nonlinear switched distributed parameter systems (DPSs) subject to time-varying delay. Initially, the original nonlinear DPSs are accurately described by Takagi-Sugeno fuzzy model in a local region. On the basis of parallel distributed compensation technique, mode-dependent fuzzy proportional and fuzzy proportional-spatial-derivative controllers are constructed, respectively. Subsequently, using single Lyapunov-Krasovskii functional and some matrix inequality methods, sufficient conditions that guarantee the stability and dissipativity of the closed-loop systems are presented in the form of linear matrix inequalities, which allow the control gain matrices to be easily obtained. Finally, numerical examples are provided to demonstrate the validity of the designed controllers.

Late‐lumping fuzzy boundary geometric control of nonlinear partial differential systems

“…Particularly, the Takagi‐Sugeno (T‐S)‐type fuzzy model has shown a proven universal approximation capability 37,38,41,53‐55 and, hence, becomes a computationally attractive solution to many nonlinear modeling problems. This even holds for nonlinear PDE systems modeling with regard to the growing number of related studies 19,43 . To construct T‐S fuzzy models for PDE systems, one may resort to exact methods such as the sector nonlinearity approach 20,38 or approximation methods, 6,24,39,40,46,56 to only cite these common fuzzy modeling methods.…”

“…On this issue, T‐S type fuzzy modeling has provided attractive solutions to many nonlinear modeling problems by involving local linear dynamics that are represented by linear PDE models. Based on this reasoning, promising findings have been achieved following either the early lumping approach 6,39‐41 or the late lumping approach 12,13,17,19‐21,42‐44,56 …”

“…On the other hand, fuzzy control problem of nonlinear parabolic PDE systems under state constraints has been investigated in Reference 39 The constrained fuzzy controller has been developed based on a T‐S fuzzy model, which describes the dynamics of the dominant modes of the PDE system in terms of finite‐dimensional model representation. T‐S fuzzy modeling has also been applied in the work by Song et al 43 to a class of switched DPSs with time‐varying delay. Based on the time‐delayed T‐S fuzzy model, mode‐dependent fuzzy controllers have been developed using parallel distributed compensation technique.…”

Robust H∞ Feedback Compensator Design for Linear Parabolic DPSs with Pointwise/Piecewise Control and Pointwise/Piecewise Measurement

“…Sampled-data boundary control and sliding mode boundary control of DPSs have been studied in [27,28], where a sampled-data strategy for the boundary control problem is proposed. Fuzzy boundary control based on the T-S fuzzy DPS model is shown in [29,30]. H ∞ boundary control has been proposed in [31] that a linear matrix inequality (LMI) approach has been utilized.…”