Stable and robust fuzzy control for uncertain nonlinear systems

Abstract

Abstract-This paper presents the stability and robustness analysis for multivariable fuzzy control systems subject to parameter uncertainties based on a single-grid-point (SGP) approach. To perform the analysis, we represent a multivariable nonlinear system using a TS-fuzzy plant model. Three design approaches of fuzzy controllers are introduced to close the feedback loop. By estimating the matrix measures of the system parameters and parameter uncertainties, stability and robustness conditions for different cases are derived. Application examples will be given to show the design procedures and the merits of the proposed fuzzy controller.Index Terms-fuzzy control, nonlinear system robustness, parameter uncertainty, stability.

Non-Fragile Dynamic Output Feedback Control Design for Fuzzy Stochastic Systems

“…Many results on the state feedback controller design method based on Takagi-Sugeno fuzzy model have appeared in the literature(for example, [2], [3], [5], [6], [7], and references therein.). The state feedback control is simple and easy to apply to controlled systems theoretically.…”

“…The first state feedback controller was designed via parallel distributed compensator(PDC) concept in [2] and [3]. The paper [5] uses a state feedback PDC, whose membership functions are mismatched with local controlled systems, and gives less conservative stability conditions than those of [2], [3], and [7]. The paper [6] recently provided a state feedback control method by iterative technique but still needs much computational load.…”

Fault Detection and Isolation of an Aircraft Turbojet Engine Using a Multi-Sensor Network and Multiple Model Approach

“…Consequently, any potential failure of an aircraft engine could cause even more extensive damages, therefore the issue of safety and reliability come to the fore. It is essential to detect faults as fast as possible and to ensure that they do not affect the control of nonlinear systems [1,2,3], especially systems like aircraft engines, where failures can be disastrous [4,5]. Advances in diagnostic systems offer better opportunities for the use of new progressive methods [6,7].…”

Nonlinear state feedback controller for nonlinear systems: Stability analysis and design based on fuzzy plant model

“…For simplicity, we write as and as . From (2) and (5) and the property that , the nonlinear control system becomes (8) where (9) To investigate the stability of (8), we employ the following Lyapunov function in quadratic form: (10) where denotes the transpose of a vector or matrix and is a symmetric positive definite matrix. Differentiating (10), we have (11) From (8) and (11), we have (12) Let (13) From (12) (14) We design the nonlinear gains in (7) as shown in (15) and (16) From Lemma 1, we can see that the number of LMI conditions is .…”