A Non-Fragile H∞ Output Feedback Controller for Uncertain Fuzzy Dynamical Systems with Multiple Time-Scales

Abstract

Abstract:This paper determines the designing of a non-fragile H ∞ output feedback controller for a class of nonlinear uncertain dynamical systems with multiple timescales described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop a non-fragile H ∞ output feedback controller which guarantees the L 2 -gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value for this class of uncertain fuzzy dynamical systems with multiple time-scales. A numerical example is provided to illustrate the design developed in this paper.

H∞Fuzzy State‐Feedback Control Plus State‐Derivative‐Feedback Control Synthesis for Photovoltaic Systems

“…Matrices I þ B i K d j À Á ∀i; j ¼ 1; 2; …; r have full rank; 2. The system (29) with the fuzzy controller (28) is asymptotically stable and an H ∞ performance is satisfied for all admissible values base on the sufficient condition for a prescribed scalarγ > 0 [8].…”

“…H ∞ dynamic feedback controller designs for complex nonlinear systems are presented in , which can be represented by TS fuzzy systems. In , for example, the existing sufficient conditions of an H ∞ fuzzy state‐feedback control are obtained from an LMI method. The application of an H ∞ fuzzy state‐feedback controller for wind energy conversion systems is shown in .…”

Control of HIV/AIDS infection system with drug dosages design via robust H ∞ fuzzy controller

“…together withC 1 i andD 12 i as shown in (10). By integrating both sides of (14) and using the fact that…”

“…Although, there exist a number of successes in using fuzzy system, many basic issues still remain to be considered. Currently, a nonlinear system which is described by a Takagi-Sugeno fuzzy model has been extensively studied; see [8][9][10][11]. Actually, the TS fuzzy model is a family set of linear models which are easily combined via nonlinear fuzzy membership functions.…”

Further results on robust fuzzy dynamic systems with LMI D-stability constraints

“…So far, there have been numerous research advances devoted to the design of an H ∞ fuzzy controller for a class of nonlinear systems which can be represented by a Takagi-Sugeno (TS) fuzzy model (see Yakubovich, 1967a;Han and Feng, 1998;Han et al, 2000;Tanaka et al, 1996;Assawinchaichote and Nguang, 2004a;2004b;2006;Assawinchaichote, 2012;Yeh et al, 2012). Fuzzy system theory utilizes qualitative, linguistic information for a complex nonlinear system to construct a mathematical model for it.…”