Robust $H_{\infty}$ Fuzzy Control for a Class of Uncertain Discrete Fuzzy Bilinear Systems

Li, T.-H.S.; Tsai, Shun-Hung; Lee, Jia-Zhen; Hsiao, Ming-Ying; Chao, Chin-Jung

doi:10.1109/tsmcb.2007.914706

Cited by 70 publications

(47 citation statements)

References 46 publications

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“…This will lead to very heavy computational burden. According to the advantages of bilinear systems and T-S fuzzy control, so many researchers paid their attentions to the T-S fuzzy models with bilinear rule consequence [16][17][18]. From these papers, it is evident that the T-S fuzzy bilinear model may be suitable for some classes of nonlinear plants.…”

Section: Introductionmentioning

confidence: 99%

“…The results therein are not applicable to systems with input delay. Recently, some controller design approaches have been presented for systems with input delay, see [2,3,4,18,[24][25][26][27][28][29][30][31][32] for fuzzy T-S systems and [8,15,33,34] for non-fuzzy systems and the references therein. All of these results are required to know the exact delay values in the implementation.…”

Section: Introductionmentioning

confidence: 99%

“…Ref. [18] presented robust stabilization for a class of discrete-time fuzzy bilinear system. Very recently, a class of nonlinear systems is described by T-S fuzzy models with nonlinear local models in Ref.…”

mentioning

confidence: 99%

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Non-Fragile Guaranteed Cost Control of Nonlinear Systems with Different State and Input Delays Based on T-S Fuzzy Local Bilinear Models

Li¹,

Li²,

Duan³

2017

Modern Fuzzy Control Systems and Its Applications

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This paper focuses on the non-fragile guaranteed cost control problem for a class of TakagiSugeno (T-S) fuzzy time-varying delay systems with local bilinear models and different state and input delays. A non-fragile guaranteed cost state-feedback controller is designed such that the closed-loop T-S fuzzy local bilinear control system is delay-dependent asymptotically stable, and the closed-loop fuzzy system performance is constrained to a certain upper bound when the additive controller gain perturbations exist. By employing the linear matrix inequality (LMI) technique, sufficient conditions are established for the existence of desired non-fragile guaranteed cost controllers. The simulation examples show that the proposed approach is effective and feasible.Keywords: fuzzy control, non-fragile guaranteed cost control, delay-dependent, linear matrix inequality (LMI), T-S fuzzy bilinear model IntroductionIn recent years, T-S (Takagi-Sugeno) model-based fuzzy control has attracted wide attention, essentially because the fuzzy model is an effective and flexible tool for the control of nonlinear systems [1][2][3][4][5][6][7][8]. Through the application of sector nonlinearity approach, local approximation in fuzzy partition spaces or other different approximation methods, T-S fuzzy models will be used to approximate or exactly represent a nonlinear system in a compact set of state variables. The merit of the model is that the consequent part of a fuzzy rule is a linear dynamic subsystem, which makes it possible to apply the classical and mature linear systems theory to nonlinear systems. Further, by using the fuzzy inference method, the overall fuzzy model will © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. be obtained. A fuzzy controller is designed via the method titled 'parallel distributed compensation (PDC) ' [3-6], the main idea of which is that for each linear subsystem, the corresponding linear controller is carried out. Finally, the overall nonlinear controller is obtained via fuzzy blending of each individual linear controller. Based on the above content, T-S fuzzy model has been widely studied, and many results have been obtained [1][2][3][4][5][6][7][8]. In practical applications, time delay often occurs in many dynamic systems such as biological systems, network systems, etc. It is shown that the existence of delays usually becomes the source of instability and deteriorating performance of systems [3][4][5][6][7][8]. In general, when delay-dependent results were calculated, the emergence of the inner product between two vectors often makes the process of calculation more complicated. In order to avoid it, some model transformations were utilized in many papers, unfortunately, which will arouse the generation of an inequality, resulting in possible conse...

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Non-Fragile Guaranteed Cost Control of Nonlinear Systems with Different State and Input Delays Based on T-S Fuzzy Local Bilinear Models

Li¹,

Li²,

Duan³

2017

Modern Fuzzy Control Systems and Its Applications

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“…Although both the fuzzy bilinear system and standard fuzzy system can describe nonlinear systems, a fuzzy bilinear system has the advantage of its representation with a lesser number of subsystems, which significantly reduces the conservatism in analysis and synthesis [7]. Due to its significant advantage, control problems for fuzzy bilinear systems have been considered, and many results have been given in [8][9][10][11][12][13][14][15][16]. For a controller design of fuzzy systems, a parallel distributed compensator (PDC) with a common Lyapunov function approach is conventionally employed.…”

Section: Introductionmentioning

confidence: 99%

A New Observer Design for Fuzzy Bilinear Systems with Unknown Inputs

Yoneyama

2017

Designs

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An observer design for a class of nonlinear systems with unknown inputs is considered. Takagi-Sugeno fuzzy bilinear systems represent a wide class of nonlinear systems, and these systems with unknown inputs are an ideal model for many physical systems. For such systems, a design method for obtaining an observer that estimates the state of the system is proposed. A parallel distributed observer (PDO), which is constructed with local linear observers and the appropriate grade of the membership functions, is a conventional observer for Takagi-Sugeno fuzzy bilinear systems. However, it is known that its design conditions have conservativeness. In this paper, to reduce the conservatism in the design conditions, non-PDO with new design conditions is proposed. Our design conditions are derived from a multiple Lyapunov function, which depends on the membership function with time-delay in the premise variables. This method eventually reduces the conservatism and enables us to construct an observer for a wide class of nonlinear systems. When the premise variables are the state variables that are not measurable, Takagi-Sugeno fuzzy bilinear systems can represent a wider class of nonlinear systems. Hence, an observer design for fuzzy bilinear systems with unmeasurable premise variables is also proposed. Finally, numerical examples are given to illustrate our design methods.

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“…The robust stabilization for continuoustime fuzzy system with local bilinear model was studied in [22], and then the result was extended to the fuzzy system with time-delay only in the state [23]. The problem of robust stabilization for discrete-time fuzzy system with local bilinear model was investigated in [24]. Reference [25] focuses on the problem of nonfragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Stabilization Control for a Class of Complex Nonlinear Systems Based on T-S Fuzzy Bilinear Model

Xing

Shi

2015

Mathematical Problems in Engineering

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This paper proposes a stable adaptive fuzzy control scheme for a class of nonlinear systems with multiple inputs. The multiple inputs T-S fuzzy bilinear model is established to represent the unknown complex systems. A parallel distributed compensation (PDC) method is utilized to design the fuzzy controller without considering the error due to fuzzy modelling and the sufficient conditions of the closed-loop system stability with respect to decay rate are derived by linear matrix inequalities (LMIs). Then the errors caused by fuzzy modelling are considered and the method of adaptive control is used to reduce the effect of the modelling errors, and dynamic performance of the closed-loop system is improved. By Lyapunov stability criterion, the resulting closed-loop system is proved to be asymptotically stable. The main contribution is to deal with the differences between the T-S fuzzy bilinear model and the real system; a global asymptotically stable adaptive control scheme is presented for real complex systems. Finally, illustrative examples are provided to demonstrate the effectiveness of the results proposed in this paper.

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Robust $H_{\infty}$ Fuzzy Control for a Class of Uncertain Discrete Fuzzy Bilinear Systems

Cited by 70 publications

References 46 publications

Non-Fragile Guaranteed Cost Control of Nonlinear Systems with Different State and Input Delays Based on T-S Fuzzy Local Bilinear Models

Non-Fragile Guaranteed Cost Control of Nonlinear Systems with Different State and Input Delays Based on T-S Fuzzy Local Bilinear Models

A New Observer Design for Fuzzy Bilinear Systems with Unknown Inputs

Adaptive Stabilization Control for a Class of Complex Nonlinear Systems Based on T-S Fuzzy Bilinear Model

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