Relaxed stability conditions based on Taylor series membership functions for polynomial fuzzy-model-based control systems

Abstract

In this paper, we investigate the stability of polynomial fuzzy-model-based (PFMB) control systems, aiming to relax stability conditions by considering the information of membership functions. To facilitate the stability analysis, we propose a general form of approximated membership functions, which is implemented by Taylor series expansion. Taylor series membership functions (TSMF) can be brought into stability conditions such that the relation between membership grades and system states is expressed. To further reduce the conservativeness, different types of information are taken into account: the boundary of membership functions, the property of membership functions, and the boundary of operating domain. Stability conditions are obtained from Lyapunov stability theory by sum of squares (SOS) approach. Simulation examples demonstrate the effect of each piece of information.

Event-Triggered Fault Detection of Nonlinear Networked Systems

“…In this paper, we will use the Taylor series approach which is represented in [59] to obtain the polynomial approximated membership functions…”

“…As represented in [59], let the error between the original membership function and the polynomial approximated membership function be ∆m ij = m ij −m ij . Denote the lower and upper bounds of ∆m ij as α ij and α ij , respectively.…”

Stabilization of Interval Type-2 Polynomial-Fuzzy-Model-Based Control Systems

“…Along this line, This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/ piecewise-linear membership functions [15] and Taylor-series membership functions [16] were proposed to carry more information to facilitate the stability analysis.…”

A review on stability analysis of continuous-time fuzzy-model-based control systems: From membership-function-independent to membership-function-dependent analysis

“…Along the line of PDC design concept, stability conditions in terms of SOS were obtained in [60]. Since then, a lot of research on stability analysis of PFMB control systems have been carried on and variations of SOS-based stability conditions have been obtained for different control problems, just to name a few, such as observer-based control problems [63,64,65,66,67], output-feedback control problems [68], positive control problems [69], regulation control problems [70], sampled-data control problems [71], stabilization control problems [60,72,61,73,74,75,76,77,78,79,80,81,82,83,84,85,86,11,87,88], switching control problems [79], tracking control problems [89] and etc.…”