Stable controller design for T–S fuzzy systems based on Lie algebras

Banks, Stephen P.; Gürkan, Evren; Erkmen, I.

doi:10.1016/j.fss.2005.05.003

Cited by 17 publications

(12 citation statements)

References 11 publications

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“…Consider a flexible joint robot (Banks et al, 2005)where x1 and x2 are the angular position and velocity of the first joint, and x3 and x4 are the angular position and velocity of the second joint, respectively. Furthermore, u is the torque input, I1 and I2 are the link and motor inertia, m is the mass of the link, g is the gravity constant, l is the link length, and k is the stiffness.…”

Section: Simulation Resultsmentioning

confidence: 99%

Global non-quadratic Lyapunov-based stabilization of T–S fuzzy systems: A descriptor approach

Vafamand

2020

Journal of Vibration and Control

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This article studies the problem of global stability of the Takagi–Sugeno fuzzy systems based on a novel descriptor-based non-quadratic Lyapunov function. A modified non-quadratic Lyapunov function, which comprises an integral term of the membership functions, and a modified non-parallel distributed controller constructed by constant delayed premise variables are considered that assure the global stability of the closed-loop T–S fuzzy system. The special structure of the used non-quadratic Lyapunov function results in time-delayed terms of the membership functions, instead of appearing their time derivatives, which is the well-known issue of the common non-quadratic Lyapunov functions in the literature. Also, the memory fuzzy controller is chosen such that the artificial constant delay-dependent stability analysis conditions for a non-delayed closed-loop T–S fuzzy system are formulated in terms of linear matrix inequalities. To further reduce the conservatives, some slack matrices are introduced by deploying the descriptor representation and decoupling lemmas. Moreover, the design of the robust fuzzy controller is studied through the [Formula: see text] performance criteria. The main advantages of the proposed approach are its small conservatives and the global stability analysis, which distinguish it from the state-of-the-art methods. To show the merits of the proposed approach, comparison results are provided, and two numerical case studies, namely, flexible joint robot and two-link joint robot are considered.

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Section: Simulation Resultsmentioning

confidence: 99%

Global non-quadratic Lyapunov-based stabilization of T–S fuzzy systems: A descriptor approach

Vafamand

2020

Journal of Vibration and Control

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“…Based on the aforesaid discussion, one can see that two constant matrices Z and Z are introduced for solving nonlinear matrix inequality (24). As a result, they need to be given in advance for solving the LMI (25). In general, it is not easy to determine the matrices Z and Z in advance before solving the LMI (25).…”

Section: Resultsmentioning

confidence: 99%

“…As a result, they need to be given in advance for solving the LMI (25). In general, it is not easy to determine the matrices Z and Z in advance before solving the LMI (25). By Lemma 1, if there exist a scalar ε > 0, some matrices X > 0, Q > 0, R > 0, S > 0, and Y j of appropriate dimensions such that (25) holds for two given n × n matrices Z and Z, then (25) holds for ε > 0, X > 0, Q > 0, R > 0, S > 0, Y j (j = 1, 2, .…”

Section: Resultsmentioning

confidence: 99%

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On Designing Fuzzy Controllers for a Class of Nonlinear Networked Control Systems

Jiang

Han

2008

IEEE Trans. Fuzzy Syst.

136

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This paper is concerned with controller design for a class of nonlinear networked control systems. These systems are approximated by uncertain linear networked Takagi-Sugeno (T-S) models with both network-induced delay and data packet dropout. Sufficient conditions are derived for the existence of a fuzzy controllers. Then, an iterative algorithm for the controller design is proposed. A control problem of a flexible-joint robot arm system is studied to show the effectiveness of the iterative algorithm.

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“…In [4], the stable control approach via T-S fuzzy model based on Lie algebras is introduced for singlelink flexible joint robot. In [5], sliding mode control approach is employed for two-degree rigid robot.…”

Section: Introductionmentioning

confidence: 99%

Stability Control of Flexible Joint Robot Based T-S Fuzzy Model Using Fuzzy Lyapunov Function

Zhang¹

2013

JCIT

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In this paper, a stability control approach of flexible joint robot (FJR) based T-S fuzzy model using fuzzy Lyapunov function is proposed. First, the Takagi and Sugeno (T-S) fuzzy model is employed to approximate the flexible joint robot, then a fuzzy controller is developed based on parallel distributed compensation principle (PDC). The non-quadratic stability conditions for the flexible joint robot control system are proposed by using fuzzy Lyapunov function combined with linear matrix inequality (LMI). Finally, the simulation example is given to illustrate the effectiveness of the proposed method.

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Stable controller design for T–S fuzzy systems based on Lie algebras

Cited by 17 publications

References 11 publications

Global non-quadratic Lyapunov-based stabilization of T–S fuzzy systems: A descriptor approach

Global non-quadratic Lyapunov-based stabilization of T–S fuzzy systems: A descriptor approach

On Designing Fuzzy Controllers for a Class of Nonlinear Networked Control Systems

Stability Control of Flexible Joint Robot Based T-S Fuzzy Model Using Fuzzy Lyapunov Function

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