Membership‐Function‐Dependent Stability Analysis of Interval Type‐2 Polynomial Fuzzy‐Model‐Base Control Systems

Abstract

Abstract:In this paper, the stability analysis for interval type-2 (IT2) polynomial fuzzy-model-based (PFMB) control system using the information of membership functions is investigated. In order to tackle uncertainties, IT2 membership functions are used in the IT2 polynomial fuzzy model and IT2 polynomial fuzzy controller. To improve the design flexibility and reduce the implementation costs, the IT2 polynomial fuzzy controller does not need to share the same premise membership functions nor the same number of rules with the IT2 polynomial fuzzy model. The stability of IT2 PFMB control system is investigated based on the Lyapunov stability theory and both sets of membership function independent (MFI) and membership function dependent (MFD) stability conditions are derived on the basis of the sum-of-squares (SOS) approach. To make the stability conditions membership function dependent, the boundary information of IT2 membership functions is used in the stability analysis. To extract richer information of IT2 membership functions, the operating domain is partitioned into sub-domains. In each sub-domain, the boundary information of IT2 membership functions and those of the upper and lower membership function are obtained. Furthermore, to further relax the conservativeness, a switching polynomial fuzzy controller, together with the informations obtained in each sub-domain, is employed in investigating the stability analysis. Numerical Examples and simulation results are given to demonstrate the validity of MFD and MFD switching methods.

Membership‐function‐dependent security control for networked T‐S fuzzy‐model‐based systems against DoS attacks

“…Fortunately, the fuzzy-model-based (FMB) method can be applied to approximate non-linear systems by connecting multiple local linear systems with non-linear membership functions (MFs) [1,2]. Due to its strong modeling ability, the FMB control has been widely concerned by scholars in [3][4][5][6][7][8][9][11][12][13][14]. In [5], the fault-tolerant controller is designed for a general polynomial FMB system.…”

Membership‐dependent stability analysis of discrete‐time positive polynomial fuzzy‐model‐based control systems with time delay

“…For the modelling of such systems, instead of using the popular Takagi–Sugeno (T–S) fuzzy model [7, 8, 18, 19], we employ polynomial fuzzy model whose subsystems are weighted by polynomial terms with corresponding membership functions to represent the dynamics of discrete time non‐linear positive system with time delay. The reason is that compared with T–S fuzzy model, polynomial fuzzy model can represent wider non‐linear systems [20–22]. In the polynomial fuzzy model, the original non‐linear components of the polynomial terms are kept intact which in turn decreases the number of fuzzy rules.…”

Model-Based Control and Stability Analysis of Discrete-Time Polynomial Fuzzy Systems With Time Delay and Positivity Constraints

“…Non-PDC technique is proposed to remove such constraint when designing fuzzy rules for the controller [29]- [31]. Membership functions and premise variables play important roles for relaxing the stability conditions [31]- [34], [42], [43]. To relax the stability conditions for positive continuous fuzzy-model-based control systems with time delay, a few attempts have been made to introduce the information of membership functions in the stability analysis [29], [30].…”