Robust reliableH_∞optimization control for uncertain discrete‐time Takagi–Sugeno fuzzy systems with time‐varying delay

Abstract

In this article, the problems of robust reliable H∞ optimization control for discrete‐time nonlinear systems with or without time‐delay subject to faults are investigated. A static state feedback controller is explored for Takagi–Sugeno fuzzy systems against nonlinear dynamics, exogenous disturbances, and model uncertainties. In contrast to the design of conventional controllers, the proposed controller is easier and more flexible. The Lyapunov function is utilized to assure the stability of the closed‐loop systems. Besides, linear matrix inequalities are utilized to derive the sufficient conditions by MATLAB toolbox. Finally, two simulation examples are shown to validate the feasibility of the suggested approach.

Robust control for uncertain variable fractional order differential systems considering time‐varying delays and nonlinear perturbations

“…This section presents two theorems in terms of several LMIs for the stability analysis of the variable fractional order time-varying delayed differential system (17). Theorem 1 proves the asymptotic stability of the system without uncertainties (ΔA(t) = ΔA 0 (t) = 0).…”

“…Theorem 1 proves the asymptotic stability of the system without uncertainties (ΔA(t) = ΔA 0 (t) = 0). Theorem 2 discusses the robust stabilization of the uncertain system (17). The controller gain matrix K must satisfy the demand of systemic stability and can also be derived from the following LMIs.…”

“…Then, the system (17) involving uncertainties is robustly stable. Besides, the stabilizing state feedback gain matrix can be obtained by K = UX −T .…”

“…The passivity analysis of fractional order neural networks with a time-varying delay based on the Razumikhin fractional order theorem is discussed by Sau et al, 14 Badri et al, 15 and Chen et al 16 investigated the robust stability and stabilization analysis of fractional order systems with time-varying delays. The problems of robust reliable H∞ optimization control for uncertain discrete-time nonlinear Takagi-Sugeno fuzzy systems with or without time-varying delay subject to faults are investigated by Sun et al 17 Zhang et al 18 discussed the asymptotic stability of the Riemann-Liouville fractional order neural networks with discrete and distributed delays. For fractional order system with time delay, the uncertainties of the system include coefficient uncertainty and interval uncertainty, have attracted much attention.…”

A fuzzy model predictive controller for stick‐slip type piezoelectric actuators

“…Based on this model, a fuzzy model predictive controller is designed for the sub-step control phase to realize the precise control of the end-effector. Unfortunately, the stability analysis is usually based on several specific assumptions 42,43 and the systems in practice cannot satisfy these conditions in most cases, which also occurs in this article and cannot be fully solved. Therefore, this article introduces an experimentally validated algorithm to the engineers working in the field of SSPEAs.…”