Stability analysis of the simplest Takagi–Sugeno fuzzy control system using circle criterion

Ban, Xiaojuan; Gao, Xueshan; Huang, Xin; Vasilakos, Athanasios V.

doi:10.1016/j.ins.2007.03.014

Cited by 60 publications

(20 citation statements)

References 23 publications

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“…Therefore, the proposed controller output is bounded between the minimum and the maximum values. Consequently, we can apply the stability criteria of [4] and [39] to demonstrate the stability of the system.…”

Section: System Stability With Fuzzy Controllermentioning

confidence: 99%

Energy-Efficient Multiobjective Thermal Control for Liquid-Cooled 3-D Stacked Architectures

Sabry

Coskun

Atienza

et al. 2011

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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Section: System Stability With Fuzzy Controllermentioning

confidence: 99%

Energy-Efficient Multiobjective Thermal Control for Liquid-Cooled 3-D Stacked Architectures

Sabry

Coskun

Atienza

et al. 2011

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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“…For the T-S fuzzy PID control systems, the analytical structure analysis is explored in [16,17], where the results show that a T-S fuzzy PID controller is a nonlinear PID controller with variable gains. The stability analysis of T-S fuzzy PID control systems is investigated based on the small gain theorem [17], the passivity theory [18], the describing function method [19], and the circle criterion [20,21], respectively. The T-S fuzzy PID controllers are applied to human arterial pressure control [16] and motor control [22].…”

Section: Introductionmentioning

confidence: 99%

“…The T-S fuzzy PID controllers are applied to human arterial pressure control [16] and motor control [22]. It is worth noting that the controlled plants in [16,[18][19][20][21][22] are linear systems rather than nonlinear systems. In [23], a neural networkbased learning method is used for tuning the parameters of the fuzzy PID controllers.…”

Section: Introductionmentioning

confidence: 99%

fuzzy PID control synthesis for Takagi–Sugeno fuzzy systems

Cao

Gao

Lam

et al. 2016

IET Control Theory & Applications

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This paper proposes a kind of H ∞ fuzzy PID control synthesis method for Takagi-Sugeno (T-S) fuzzy systems. The basic idea of the presented method is to transform the fuzzy PID controller design problem into that of the fuzzy static output feedback (SOF) controller design. Based on an iterative linear matrix inequality (ILMI) algorithm, the fuzzy SOF control laws can be obtained. After that, the fuzzy PID controller is recovered from the fuzzy SOF controller. Simulation examples are given to show the effectiveness of the proposed method.

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“…Parallel to the Mamdani fuzzy PID control systems, the stability analysis and controller design of the T-S fuzzy PID control systems have been investigated as well. Based on the circle criterion, the stability conditions for the T-S fuzzy proportional and fuzzy PI control systems are proposed and explored in [10] and [11], respectively. The analytical structures of the T-S fuzzy PI and fuzzy PD controllers are examined in [12], and the BIBO stability condition is given on the basis of the small gain theorem.…”

Section: Introduction (Heading 1)mentioning

confidence: 99%

Stability analysis of T-S fuzzy PD, PI, and PID control systems

Cao

Gao

Wang³

et al. 2015

2015 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD)

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Abstract-In this paper, simple and systematic ways of designing stabilization fuzzy PID (Proportional-Integral-Differential), PI (Proportional-Integral), and PD (Proportional-Differential) controllers for the Takagi-Sugeno fuzzy model are proposed. The state space representations of the fuzzy PID, PI, and PD controllers are firstly presented. Then we equivalently transform the fuzzy PID (PI, or PD) control system into the fuzzy static output feedback control system. The fuzzy static output feedback controller design for the latter system can be efficiently solved via the existing numerical optimization methods with some conservatism. Consequently, the fuzzy PID (PI, or PD) controller can be derived due to the one-to-one correspondence between the fuzzy PID controller and the fuzzy static output feedback controller. A simulation example is also given to demonstrate the effectiveness of our proposed methods.

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Stability analysis of the simplest Takagi–Sugeno fuzzy control system using circle criterion

Cited by 60 publications

References 23 publications

Energy-Efficient Multiobjective Thermal Control for Liquid-Cooled 3-D Stacked Architectures

Energy-Efficient Multiobjective Thermal Control for Liquid-Cooled 3-D Stacked Architectures

fuzzy PID control synthesis for Takagi–Sugeno fuzzy systems

Stability analysis of T-S fuzzy PD, PI, and PID control systems

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