Fuzzy controller design for Takagi–Sugeno fuzzy models with multiplicative noises via relaxed non-quadratic stability analysis

This paper deals with the problem of stability analysis and stabilization via Takagi-Sugeno (T-S) fuzzy models for nonlinear time-delay systems. First, Takagi-Sugeno (T-S) fuzzy models and some stability results are recalled. To design fuzzy controllers, nonlinear time-delay systems are represented by Takagi-Sugeno fuzzy models. The concept of parallel-distributed compensation (PDC) is employed to determine structures of fuzzy controllers from the T-S fuzzy models. LMI-based design problems are defined and employed to find feedback gains of fuzzy controller and common positive definite matrices P satisfying stability a delay-dependent stability criterion derived in terms of Lyapunov direct method. Based on the control scheme and this criterion, a fuzzy controller is then designed via the technique of PDC to stabilize the nonlinear time-delay system and the H∞ control performance is achieved in the mean time. Finally, the proposed controller design method is demonstrated through numerical simulations on the chaotic and resonant systems.

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Actuator Saturated Fuzzy Controller Design for Interval Type-2 Takagi-Sugeno Fuzzy Models with Multiplicative Noises

Processes ◽

10.3390/pr9050823 ◽

2021 ◽

Vol 9 (5) ◽

pp. 823

Author(s):

Wen-Jer Chang ◽

Yu-Wei Lin ◽

Yann-Horng Lin ◽

Chin-Lin Pen ◽

Ming-Hsuan Tsai

Keyword(s):

Nonlinear Systems ◽

Fuzzy Controller ◽

Controller Design ◽

Actuator Saturation ◽

Design Method ◽

Fuzzy Model ◽

The Stability ◽

Interval Type ◽

Takagi Sugeno

In many practical systems, stochastic behaviors usually occur and need to be considered in the controller design. To ensure the system performance under the effect of stochastic behaviors, the controller may become bigger even beyond the capacity of practical applications. Therefore, the actuator saturation problem also must be considered in the controller design. The type-2 Takagi-Sugeno (T-S) fuzzy model can describe the parameter uncertainties more completely than the type-1 T-S fuzzy model for a class of nonlinear systems. A fuzzy controller design method is proposed in this paper based on the Interval Type-2 (IT2) T-S fuzzy model for stochastic nonlinear systems subject to actuator saturation. The stability analysis and some corresponding sufficient conditions for the IT2 T-S fuzzy model are developed using Lyapunov theory. Via transferring the stability and control problem into Linear Matrix Inequality (LMI) problem, the proposed fuzzy control problem can be solved by the convex optimization algorithm. Finally, a nonlinear ship steering system is considered in the simulations to verify the feasibility and efficiency of the proposed fuzzy controller design method.

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Fuzzy Controllers for Nonaffine-in-Control Singularly Perturbed Switched Systems

Mathematical Problems in Engineering ◽

10.1155/2015/896413 ◽

2015 ◽

Vol 2015 ◽

pp. 1-11 ◽

Cited By ~ 2

Author(s):

Linna Zhou ◽

Qianjin Wang ◽

Xiaoping Ma ◽

Chunyu Yang

Keyword(s):

Switched Systems ◽

Fuzzy Controller ◽

Controller Design ◽

Design Method ◽

Singularly Perturbed ◽

Dynamic State ◽

Linear Matrix ◽

Closed Loop System ◽

Stability Bound ◽

Takagi Sugeno

This paper investigates the problem of fuzzy controller design for nonaffine-in-control singularly perturbed switched systems (NCSPSSs). First, the NCSPSS is approximated by Takagi-Sugeno (T-S) models which include not only state but also control variables in the premise part of the rules. Then, a dynamic state feedback controller design method is proposed in terms of linear matrix inequalities. Under the controller, stability bound estimation problem of the closed-loop system is solved. Finally, an example is given to show the feasibility and effectiveness of the obtained methods.

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Stability Analysis and Nonlinear Observer Design Using Takagi-Sugeno Fuzzy Models

10.1007/978-3-642-16776-8 ◽

2011 ◽

Cited By ~ 30

Author(s):

Zsófia Lendek ◽

Thierry Marie Guerra ◽

Robert Babuška ◽

Bart De Schutter

Keyword(s):

Stability Analysis ◽

Observer Design ◽

Nonlinear Observer ◽

Fuzzy Models ◽

Takagi Sugeno

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DELAYED FUZZY CONTROLLER DESIGN FOR HYPERCHAOS WITH APPLICATION TO HYPERCHAOTIC CHEN'S SYSTEM

International Journal of Modern Physics C ◽

10.1142/s0129183107011157 ◽

2007 ◽

Vol 18 (07) ◽

pp. 1095-1105 ◽

Cited By ~ 10

Author(s):

XINGWEN LIU ◽

XIN GAO

Keyword(s):

Fuzzy Controller ◽

Controller Design ◽

Fuzzy Model ◽

Linear Matrix ◽

Delayed State Feedback ◽

Delay Dependent ◽

Takagi Sugeno ◽

Compensation Design ◽

Hyperchaotic Systems ◽

Control Criterion

Studied in this paper is the control problem of hyperchaotic systems. By combining Takagi–Sugeno (T–S) fuzzy model with parallel distributed compensation design technique, we propose a delay-dependent control criterion via pure delayed state feedback. Because the result is expressed in terms of linear matrix inequalities (LMIs), it is quite convenient to check in practice. Based on this criterion, a procedure is provided for designing fuzzy controller for such systems. This method is a universal one for controlling continuous hyperchaotic systems. As illustrated by its application to hyperchaotic Chen's system, the controller design is quite effective.

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STABILITY ANALYSIS OF NONLINEAR INTERCONNECTED SYSTEMS VIA T–S FUZZY MODELS

International Journal of Computational Intelligence and Applications ◽

10.1142/s1469026804001033 ◽

2004 ◽

Vol 04 (01) ◽

pp. 41-55 ◽

Cited By ~ 7

Author(s):

WEI-LING CHIANG ◽

CHENG-WU CHEN ◽

FENG-HSIAG HSIAO

Keyword(s):

Stability Analysis ◽

Lyapunov Functions ◽

Direct Method ◽

Interconnected Systems ◽

Linear Matrix ◽

Matrix Inequality ◽

Fuzzy Models ◽

Fuzzy Techniques ◽

The Stability ◽

Takagi Sugeno

This paper is concerned with the stability problem of nonlinear interconnected systems. Each of them consists of a few interconnected subsystems which are approximated by Takagi–Sugeno (T–S) type fuzzy models. In terms of Lyapunov's direct method, a stability criterion is derived to guarantee the asymptotic stability of interconnected systems. It is shown that the stability analysis problems of nonlinear interconnected systems can be reduced to linear matrix inequality (LMI) problems via suitable Lyapunov functions and T–S fuzzy techniques. Finally, numerical examples with simulations are given to demonstrate the validity of the proposed approach.

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