T–S Fuzzy Bilinear Model and Fuzzy Controller Design for a Class of Nonlinear Systems

Li, T.-H.S.; Tsai, Shun-Hung

doi:10.1109/tfuzz.2006.889964

Cited by 113 publications

(58 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…According to these equilibrium points, [x e u e ], which are also chosen as the desired operating points, ½x 0 e u 0 e , we can use the similar modeling method that is described in Ref. [16]. …”

Section: Simulation Examplesmentioning

confidence: 99%

See 1 more Smart Citation

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

View full text Add to dashboard Cite

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...

show abstract

Section: Simulation Examplesmentioning

confidence: 99%

“…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.…”

mentioning

confidence: 99%

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

View full text Add to dashboard Cite

show abstract

“…was firstly presented by Li and Tsai (2007), and stability conditions of the system were given via LMIs. also presented robust fuzzy controllers for a class of discrete-time T-S fuzzy bilinear systems, in which the parallel distributed compensation method was utilized to design a fuzzy controller to ensure robust asymptotic stability of the closed-loop system and to guarantee an H ∞ norm-bound constraint on disturbance attenuation for all admissible uncertainties.…”

Section: R Duan Et Almentioning

confidence: 99%

Stability analysis and H_∞ control of discrete T–S fuzzy hyperbolic systems

Duan

Zhang

et al. 2016

International Journal of Applied Mathematics and Computer Science

View full text Add to dashboard Cite

This paper focuses on the problem of constraint control for a class of discrete-time nonlinear systems. Firstly, a new discrete T-S fuzzy hyperbolic model is proposed to represent a class of discrete-time nonlinear systems. By means of the parallel distributed compensation (PDC) method, a novel asymptotic stabilizing control law with the "soft" constraint property is designed. The main advantage is that the proposed control method may achieve a small control amplitude. Secondly, for an uncertain discrete T-S fuzzy hyperbolic system with external disturbances, by the proposed control method, the robust stability and H∞ performance are developed by using a Lyapunov function, and some sufficient conditions are established through seeking feasible solutions of some linear matrix inequalities (LMIs) to obtain several positive diagonally dominant (PDD) matrices. Finally, the validity and feasibility of the proposed schemes are demonstrated by a numerical example and a Van de Vusse one, and some comparisons of the discrete T-S fuzzy hyperbolic model with the discrete T-S fuzzy linear one are also given to illustrate the advantage of our approach.

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

T–S Fuzzy Bilinear Model and Fuzzy Controller Design for a Class of Nonlinear Systems

Cited by 113 publications

References 39 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

Stability analysis and H_∞ control of discrete T–S fuzzy hyperbolic systems

A New Observer Design for Fuzzy Bilinear Systems with Unknown Inputs

Contact Info

Product

Resources

About

T–S Fuzzy Bilinear Model and Fuzzy Controller Design for a Class of Nonlinear Systems

Cited by 113 publications

References 39 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

Stability analysis and H∞ control of discrete T–S fuzzy hyperbolic systems

A New Observer Design for Fuzzy Bilinear Systems with Unknown Inputs

Contact Info

Product

Resources

About

Stability analysis and H_∞ control of discrete T–S fuzzy hyperbolic systems