Further Studies on Stability and Stabilization of T‐S Fuzzy Systems With Time‐Varying Delays via Fuzzy Lyapunov‐Krasovskii Functional Method

Tan, Jiyong; Dian, Songyi; Zhao, Tao

doi:10.1002/asjc.1697

Cited by 14 publications

(6 citation statements)

References 50 publications

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“…Therefore, the solution of Theorem 2 was obtained by solving the MATLAB LMI toolbox (23), and the controller gains K 1 , K 2 and observer gains L 1 , L 2 are as follows: Â Ã According to (10), the controller is written as:…”

Section: Simulation Parameter Settingmentioning

confidence: 99%

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Torque tracking control of electric load simulator with active motion disturbance and nonlinearity based on T‐S fuzzy model

Pan

Wang

2018

Asian Journal of Control

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This paper develops a high performance nonlinear control method for an electric load simulator (ELS). The tracking performance of the ELS is mainly affected by the actuator's active motion disturbance and friction nonlinearity. First, a nonlinear model of ELS is developed, and then the Takagi-Sugeno fuzzy model is used to represent the friction nonlinearity ofthe ELS. A state observer is constructed to estimate the speed of the load system. For converting the tracking control into a stabilization problem, a new control design called virtual desired state synthesis is proposed to define the internal desired states. External disturbances are attenuated based on an H ∞ criterion and the stability of the entire closed-loop model is investigated using the well-known quadratic Lyapunov function. Meanwhile, the feedback gains and the observer gains are obtained separately by solving a set of linear matrix inequalities (LMIs). Both a simulation and experiment were performed to validate the effectiveness of the developed algorithm. KEYWORDS T-S fuzzy modelH ∞ criterionelectric load simulator (ELS), linear matrix inequalities (LMIs), torque tracking control

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Section: Simulation Parameter Settingmentioning

confidence: 99%

“…By "fuzzy blending" a group of linear submodels, T-S fuzzy models have the ability to approximate a highly nonlinear dynamical system to arbitrary degreeof accuracy. A great quantity of research on systematic analysis and design of fuzzy systems has been carried out in the last decade (see,e.g., [19][20][21][22][23]).…”

mentioning

confidence: 99%

Torque tracking control of electric load simulator with active motion disturbance and nonlinearity based on T‐S fuzzy model

Pan

Wang

2018

Asian Journal of Control

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“…Proof: To begin with, let us define P (θ) = P −1 (θ) and P0 = P −1 0 . Then, condition ( 19) is converted into (30), and performing the congruent transformation to (21) (respectively, (22)) by diag(1, P (θ)) provides (31) (respectively, (32)).…”

Section: Local Stabilization Approachmentioning

confidence: 99%

“…Furthermore, it has also been verified that the non-parallel distributed compensation (non-PDC) control law can make the structure of fuzzy basis-dependent control gains more flexible (refer to [2,4,37] for details). Thus, various control synthesis methods that can exploit the strengths of non-PDC control laws and/or nonquadratic Lyapunov function approaches have been actively developed (see [1,21,29,31] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Nonquadratic local stabilization of T-S fuzzy systems via improved slack-variable-free relaxation technique under limited operating region

Kim

2022

Preprint

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This paper aims to investigate the problem of nonquadratic local stabilization and disturbance attenuation for Takagi-Sugeno (T-S) fuzzy systems under the limited operating region of premise variables. To derive less conservative local stabilization conditions, this paper first proposes a parameterized linear matrix inequality (PLMI) formulation method that enables both the nonquadratic Lyapunov function and the non-parallel distributed compensation (non-PDC) control scheme. Specifically, in the PLMI formulation, the time derivatives of fuzzy basis functions are addressed without any boundary assumptions and by avoiding excessive use of inequality constraints and slack variables. Moreover, an effective relaxation technique is proposed to obtain a finite set of LMIs from PLMIs in a less conservative way without extra slack variables. Finally, three examples are provided to illustrate the effectiveness of the proposed method.

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“…A robust FD observer is designed in Chadli et al (2013) for discrete-time T-S fuzzy systems with sensor faults and disturbances, and in Zheng et al (2006), the FD problem is solved with the aid of T-S fuzzy modeling for networked control systems with unknown Markovian delays. Stability and other control issues for T-S systems with time-varying delays are dealt in Kharrat et al (2018), Tan et al (2018), Zeng et al (2014) and Zhang et al (2009, 2016).…”

Section: Introductionmentioning

confidence: 99%

Fault-tolerant controller design with fault estimation capability for a class of nonlinear systems using generalized Takagi-Sugeno fuzzy model

Navarbaf

Khosrowjerdi

2019

Transactions of the Institute of Measurement and Control

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In this paper, a new design approach to construct a fault-tolerant controller (FTC) with fault estimation capability is proposed using a generalized Takagi-Sugeno (T-S) fuzzy model for a class of nonlinear systems in the presence of actuator faults and unknown disturbances. The generalized T-S fuzzy model consists of some local models with multiplicative nonlinear terms that satisfy Lipschitz condition. Besides covering a very wide range of nonlinear systems with a smaller number of local rules in comparison with the conventional T-S fuzzy model and hence having less computational burden, the existence of the multiplicative nonlinear term solves the uncontrollability issues that the other generalized T-S fuzzy models with additive nonlinear terms dealt with. A state/fault observer designed for the considered generalized T-S fuzzy model and then, a dynamic FTC law based on the estimated fault information is proposed and sufficient design conditions are given in terms of linear matrix inequalities (LMIs). It can be shown that the number of LMIs are less than that of previously proposed methods and then feasibility of our method is more likely. The effectiveness of the proposed FTC approach is verified using a nonlinear mass-spring-damper system.

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Further Studies on Stability and Stabilization of T‐S Fuzzy Systems With Time‐Varying Delays via Fuzzy Lyapunov‐Krasovskii Functional Method

Cited by 14 publications

References 50 publications

Torque tracking control of electric load simulator with active motion disturbance and nonlinearity based on T‐S fuzzy model

Torque tracking control of electric load simulator with active motion disturbance and nonlinearity based on T‐S fuzzy model

Nonquadratic local stabilization of T-S fuzzy systems via improved slack-variable-free relaxation technique under limited operating region

Fault-tolerant controller design with fault estimation capability for a class of nonlinear systems using generalized Takagi-Sugeno fuzzy model

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