LMI Solution for Robust Static Output Feedback Control of Discrete Takagi–Sugeno Fuzzy Models

Abstract

This paper deals with the stabilization problem of discrete-time Takagi-Sugeno (T-S) fuzzy systems via static output controller (SOFC). The proposed method uses the descriptor approach to study this problem and leads to strict Linear Matrix Inequalities (LMIs) formulation. In contrast to the existing results, the method allows coping with multiple output matrices and also uncertainties. Moreover, the new proposed method can lead to less conservative results by introducing slack variables and considering multiple Lyapunov matrices. A robust SOFC for uncertain T-S fuzzy models is also derived in strict LMIs terms. Numerical examples are given to illustrate the effectiveness of the proposed design results.

Robust fault tolerant tracking controller design for a VTOL aircraft

“…This latter can be expressed as given by (34), where 0 is a zero matrix. Since the faults affecting the system in this approach are supposed to be constant ( ( ) ) the dynamics of the fault estimation error is given by (35).…”

“…Regrettably, the design of FTC for nonlinear systems is far more complicated. Fortunately, as shown in [13], Takagi-Sugeno (T-S) fuzzy modeling concepts can be used to overcome this defect for the nonlinear plant systems [35][36]. Consequently fault tolerant controls, for several kind of T-S fuzzy model have been strongly investigated and a lot of works, involving various specifications, are now available.…”

Distributed piecewise filtering design for large-scale networked nonlinear systems

“…T-S fuzzy approach combining the merits of both fuzzy logic theory and linear system theory is successfully implemented in embedded microprocessors and is widely applied in a variety of engineering fields [10][11][12][13]. During the past few years, a great number of results on function approximation, systematic stability analysis, controller and filtering design for T-S fuzzy systems have been reported in the open literature [14][15][16][17][18][19].…”

Vehicle Fault Tolerant Control Using a Robust Output Fuzzy Controller Design

“…In the transport domain, to satisfy increasing safety, many new vehicles are equipped with different driver assisted systems such as Traction Control System (TCS) and Electronic Stabilization Program (ESP) to maintain stability and acceptable performances even when some sensors have failed. These systems use a combination of ABS information, yaw rate, wheel speed, lateral acceleration and steer angle to improve the stabilization of the vehicle in dangerous driving situations and then improve the active safety (Kienck andNielsen, 2000, Dahmani, Chadli andal, 2012).…”

“…In this paper, a fuzzy controller is designed by considering the lateral velocity estimated using a nonlinear observer. In the analysis and design, the vehicle lateral will be represented by a switching systems (Chadli and Darouach, 2011) or by a Takagi-Sugeno (T-S) fuzzy model (Takagi and Sugeno, 1985), largely used these last years (Xioodong and Qingling, 2003;Chadli, Maquin and Ragot, 2005;Kirakidis, 2001;Tanaka and Wang, 1998;Chadli and El Hajjaji, 2006;Guerra and al, 2011;Chadli and Guerra, 2012). It is usually referred to as the bicycle model.…”