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Hu G, Wang L, Liu X. A new approach to local H∞ control for continuous-time T-S fuzzy models. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2020. [DOI: 10.3233/jifs-190974] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Guolin Hu
- School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan, China
| | - Likui Wang
- School of Mathematics and Information Science, Nanchang Hangkong University, Nanchang, China
| | - Xiaodong Liu
- Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, China
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2
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Design and Implementation of the Battery Energy Storage System in DC Micro-Grid Systems. ENERGIES 2018. [DOI: 10.3390/en11061566] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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3
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Hu G, Liu X, Wang L, Li H. An extended approach to controller design of continuous-time Takagi-Sugeno fuzzy model. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2018. [DOI: 10.3233/jifs-171266] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Guolin Hu
- Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, China
| | - Xiaodong Liu
- Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, China
| | - Likui Wang
- School of Mathematics and Information Science, Nanchang Hangkong University, Nanchang, China
| | - Hongxing Li
- Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, China
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4
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Wang L, Liu J. Local stability analysis for continuous-time Takagi–Sugeno fuzzy systems with time delay. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.08.021] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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5
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Wang LK, Zhang HG, Liu XD. H∞ Observer Design for Continuous-Time Takagi-Sugeno Fuzzy Model With Unknown Premise Variables via Nonquadratic Lyapunov Function. IEEE TRANSACTIONS ON CYBERNETICS 2016; 46:1986-1996. [PMID: 27323385 DOI: 10.1109/tcyb.2015.2459016] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
This paper deals with the problem of observer design for continuous-time Takagi-Sugeno fuzzy models with unmeasurable premise variables. First, in order to improve the existing results of observer design, a new method is proposed to bound the time derivatives of the membership function. Then, by applying the nonquadratic Lyapunov function and the matrix decoupling technique, the controller gains and observer gains are designed to guarantee that the error system is asymptotically stale. Furthermore, better H ∞ performance can be obtained by solving an optimization problem. All of the results are presented as linear matrices inequalities and three examples are provided to demonstrate the merits of the proposed approach.
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6
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Zhao T, Wei Z, Dian S, Xiao J. Observer-based H∞ controller design for interval type-2 T–S fuzzy systems. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.10.074] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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7
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Wang LK, Peng JL, Liu XD, Zhang HG. An approach to observer design of continuous-time Takagi–Sugeno fuzzy model with bounded disturbances. Inf Sci (N Y) 2015. [DOI: 10.1016/j.ins.2015.06.034] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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8
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Robust stabilization of T–S fuzzy discrete systems with actuator saturation via PDC and non-PDC law. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2015.05.085] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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9
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H∞ control of continuous-time interval type-2 T–S fuzzy systems via dynamic output feedback controllers. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2015.03.002] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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10
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Asemani M, Majd VJ. A novel descriptor redundancy approach for non-quadratic robust H∞ control of T-S fuzzy nonlinear singularly perturbed systems. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2015. [DOI: 10.3233/ifs-141303] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- M.H. Asemani
- Control and Power Engineering Department, School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran
| | - Vahid Johari Majd
- Control Engineering Department, School of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, Iran
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11
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Wang L, Peng J, Liu X, Zhang H. Further study on local stabilization of continuous-time nonlinear systems presented as Takagi-Sugeno fuzzy model. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2015. [DOI: 10.3233/ifs-151594] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Likui Wang
- School of Mathematics and Information Science, Nanchang Hangkong University, Nanchang, China
| | - Jiali Peng
- School of Mathematics and Information Science, Nanchang Hangkong University, Nanchang, China
| | - Xiaodong Liu
- Research Center of Information and Control, Dalian University of Technology, Dalian, China
| | - Huaguang Zhang
- School of Information Science and Engineering, Northeastern University, Shenyang, China
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Pitarch JL, Sala A, Ariño CV. Closed-form estimates of the domain of attraction for nonlinear systems via fuzzy-polynomial models. IEEE TRANSACTIONS ON CYBERNETICS 2014; 44:526-538. [PMID: 23757565 DOI: 10.1109/tcyb.2013.2258910] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
In this paper, the domain of attraction of the origin of a nonlinear system is estimated in closed form via level sets with polynomial boundaries, iteratively computed. In particular, the domain of attraction is expanded from a previous estimate, such as a classical Lyapunov level set. With the use of fuzzy-polynomial models, the domain of attraction analysis can be carried out via sum of squares optimization and an iterative algorithm. The result is a function that bounds the domain of attraction, free from the usual restriction of being positive and decrescent in all the interior of its level sets.
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Lee DH, Kim DW. Relaxed LMI Conditions for Local Stability and Local Stabilization of Continuous-Time Takagi-Sugeno Fuzzy Systems. IEEE TRANSACTIONS ON CYBERNETICS 2014; 44:394-405. [PMID: 23757558 DOI: 10.1109/tcyb.2013.2256781] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
This paper addresses the problems of local stability analysis, local stabilization, and computation of invariant subsets of the domain of attraction for continuous-time Takagi-Sugeno fuzzy systems. Improvements on the existing stability and stabilization conditions are achieved through the reduction of conservatism. To release the conservatism further, the so-called multidimensional fuzzy summation approach is adopted. The design and analysis conditions are expressed as one-parameter minimization problems which can be solved via a sequence of linear matrix inequality optimizations or treated as eigenvalue problems. Examples are given to show the validity of the proposed method.
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Jafarzadeh S, Fadali MS. On the stability and control of continuous-time TSK fuzzy systems. IEEE TRANSACTIONS ON CYBERNETICS 2013; 43:1073-1087. [PMID: 23757442 DOI: 10.1109/tsmcb.2012.2223672] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
This paper introduces a new stability test and control design methodology for type-1 and type-2 continuous-time (CT) Takagi-Sugeno-Kang systems. Unlike methods based on a common Lyapunov function, our stability results apply for systems with unstable consequents, and our controllers can be designed for systems with unstabilizable consequents. The stability results are derived using the comparison principle with a discontinuous function and the upper right-hand derivative. The control results include CT fuzzy proportional controllers and fuzzy proportional-integral controllers that can be obtained by solving linear matrix inequalities. We provide several examples to demonstrate our stability testing and controller design and compare our results to available methods in the literature. Our results compare favorably with results available in the literature and provide stability tests and controllers where earlier approaches fail.
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Affiliation(s)
- Saeed Jafarzadeh
- Department of Computer and Electrical Engineering and Computer Science, California State University Bakersfield, Bakersfield, CA 93311, USA.
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15
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Lam H, Lauber J. Membership-function-dependent stability analysis of fuzzy-model-based control systems using fuzzy Lyapunov functions. Inf Sci (N Y) 2013. [DOI: 10.1016/j.ins.2012.12.027] [Citation(s) in RCA: 69] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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16
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Qing Gao, Xiao-Jun Zeng, Gang Feng, Yong Wang, Jianbin Qiu. T-S-Fuzzy-Model-Based Approximation and Controller Design for General Nonlinear Systems. IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS. PART B, CYBERNETICS : A PUBLICATION OF THE IEEE SYSTEMS, MAN, AND CYBERNETICS SOCIETY 2012; 42:1143-1154. [PMID: 22434816 DOI: 10.1109/tsmcb.2012.2187442] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
This paper presents a novel approach to control general nonlinear systems based on Takagi-Sugeno (T-S) fuzzy dynamic models. It is first shown that a general nonlinear system can be approximated by a generalized T-S fuzzy model to any degree of accuracy on any compact set. It is then shown that the stabilization problem of the general nonlinear system can be solved as a robust stabilization problem of the developed T-S fuzzy system with the approximation errors as the uncertainty term. Based on a piecewise quadratic Lyapunov function, the robust semiglobal stabilization and H∞ control of the general nonlinear system are formulated in the form of linear matrix inequalities. Simulation results are provided to illustrate the effectiveness of the proposed approaches.
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17
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Further studies on relaxed stabilization conditions for discrete-time two-dimension Takagi–Sugeno fuzzy systems. Inf Sci (N Y) 2012. [DOI: 10.1016/j.ins.2011.11.031] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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18
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Zhang H, Xie X, Tong S. Homogenous polynomially parameter-dependent H∞ filter designs of discrete-time fuzzy systems. IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS. PART B, CYBERNETICS : A PUBLICATION OF THE IEEE SYSTEMS, MAN, AND CYBERNETICS SOCIETY 2011; 41:1313-22. [PMID: 21606037 DOI: 10.1109/tsmcb.2011.2139203] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
This paper proposes a novel H(∞) filtering technique for a class of discrete-time fuzzy systems. First, a novel kind of fuzzy H(∞) filter, which is homogenous polynomially parameter dependent on membership functions with an arbitrary degree, is developed to guarantee the asymptotic stability and a prescribed H(∞) performance of the filtering error system. Second, relaxed conditions for H(∞) performance analysis are proposed by using a new fuzzy Lyapunov function and the Finsler lemma with homogenous polynomial matrix Lagrange multipliers. Then, based on a new kind of slack variable technique, relaxed linear matrix inequality-based H(∞) filtering conditions are proposed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approach.
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Affiliation(s)
- Huaguang Zhang
- School of Information Science and Engineering, Northeastern University, Shenyang, China.
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Husek P. Stability margin of linear systems with parameters described by fuzzy numbers. IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS. PART B, CYBERNETICS : A PUBLICATION OF THE IEEE SYSTEMS, MAN, AND CYBERNETICS SOCIETY 2011; 41:1174-82. [PMID: 21349791 DOI: 10.1109/tsmcb.2011.2112348] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
This paper deals with the linear systems with uncertain parameters described by fuzzy numbers. The problem of determining the stability margin of those systems with linear affine dependence of the coefficients of a characteristic polynomial on system parameters is studied. Fuzzy numbers describing the system parameters are allowed to be characterized by arbitrary nonsymmetric membership functions. An elegant solution, graphical in nature, based on generalization of the Tsypkin-Polyak plot is presented. The advantage of the presented approach over the classical robust concept is demonstrated on a control of the Fiat Dedra engine model and a control of the quarter car suspension model.
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Affiliation(s)
- Petr Husek
- Department of Control Engineering, Faculty of Electrical Engineering, Czech Technical University in Prague, Prague, Czech Republic.
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Li J, Zhou S, Xu S. Fuzzy Control System Design via Fuzzy Lyapunov Functions. ACTA ACUST UNITED AC 2008; 38:1657-61. [DOI: 10.1109/tsmcb.2008.928224] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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