Stability analysis and <i>H<sub>∞</sub>
                  </i> control of discrete T–S fuzzy hyperbolic systems

Duan, Ruirui; Li, Junmin; Zhang, Yanni; Yang, Ying; Chen, Guopei

doi:10.1515/amcs-2016-0009

Cited by 5 publications

(8 citation statements)

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“…Several sorts of conditions can be taken into account during the design stage (Tanaka and Wang, 2001): stability, decay rate, state and input constraints, H ∞ -norm, etc. Recently, some papers (Saifia et al, 2012;Chang and Shih, 2015;Nguyen et al, 2015;Klug et al, 2015;Duan et al, 2016;Vafamand et al, 2016) have reported research on designing fuzzy controllers for TS fuzzy models when perturbations are present and there exists actuator saturation and state 458 J.V. Salcedo et al Nguyen et al (2015; and Vafamand et al (2016) claim that they outperform previous results (Saifia et al, 2012;Chang and Shih, 2015;Klug et al, 2015).…”

Section: Introductionmentioning

confidence: 98%

Bibo Stabilisation of Continuous–Time Takagi–Sugeno Systems under Persistent Perturbations and Input Saturation

Salcedo

Martínez

García-Nieto

et al. 2018

International Journal of Applied Mathematics and Computer Science

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This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under persistent perturbations. It is assumed that all the states of the Takagi-Sugeno (TS) fuzzy model representing a non-linear system are measurable. Such controllers achieve bounded input bounded output (BIBO) stabilisation in closed loop based on the computation of inescapable ellipsoids. These ellipsoids are computed with linear matrix inequalities (LMIs) that guarantee stabilisation with input saturation and persistent perturbations. In particular, two kinds of inescapable ellipsoids are computed when solving a multiobjective optimization problem: the maximum volume inescapable ellipsoids contained inside the validity domain of the TS fuzzy model and the smallest inescapable ellipsoids which guarantee a minimum *-norm (upper bound of the 1-norm) of the perturbed system. For every initial point contained in the maximum volume ellipsoid, the closed loop will enter the minimum *-norm ellipsoid after a finite time, and it will remain inside afterwards. Consequently, the designed controllers have a large domain of validity and ensure a small value for the 1-norm of closed loop.

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Section: Introductionmentioning

confidence: 98%

Bibo Stabilisation of Continuous–Time Takagi–Sugeno Systems under Persistent Perturbations and Input Saturation

Salcedo

Martínez

García-Nieto

et al. 2018

International Journal of Applied Mathematics and Computer Science

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“…Especially, for discrete-time T-S fuzzy systems, results devoted to SOF control can be found in [5,12,18,19,21,23,24]; and especially, in [4] and [12], where a fuzzy weighting-dependent Lyapunov function (FWDLF) has been used. At last, some performances are generally to be added, H ∞ attenuation being one of the most widely used for T-S systems [8,[10][11][12][13]17,19,20,22,[25][26][27][28][29][30]. For real-time control, another important issue is the physical limitations of the actuators, such as input bounds and/or rate saturation constraints.…”

Section: Introductionmentioning

confidence: 99%

“…Many results are reported in the literature regarding stability analysis of linear (more recently, see [35][36][37][38]) and nonlinear systems [8,10,16,25,26,[31][32][33][34][40][41][42]45] subject to input constraints. Several approaches were experienced with T-S systems: bound on the initial conditions to avoid the input saturation in low gain control laws [16,26,40]; estimation of the attraction domain in the presence of actuator saturation [8,10,16,38,40,41,45]; transformation of the saturation into a dead-zone nonlinearity [8], use of a polytopic model to express the saturation constraints in [10,16,[20][21][22]25,26,[35][36][37][38][39][40][41]45].…”

Section: Introductionmentioning

confidence: 99%

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Robust H_∞ static output‐feedback control for discrete‐time fuzzy systems with actuator saturation via fuzzy Lyapunov functions

Saifia

Chadli

Labiod

et al. 2019

Asian Journal of Control

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In this paper, we present a new scheme for designing a H∞ stabilizing controller for discrete‐time Takagi‐Sugeno fuzzy systems with actuator saturation and external disturbances. The weighting‐dependent Lyapunov functions approach is used to design a robust static output‐feedback controller. To address the input saturation problem, both constrained and saturated control input cases are considered. In both cases, stabilization conditions of the fuzzy system are formulated as a convex optimization problem in terms of linear matrix inequalities. Two simulation examples are included to illustrate the effectiveness of the proposed design methods. A comparison with the results given in recent literature on the subject is also presented.

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“…In Refs. [45,46], to achieve small control amplitude, a new T-S fuzzy hyperbolic model was developed, moreover, Ref. [46] considered the input delay of the novel model.…”

Section: Introductionmentioning

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

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

Cited by 5 publications

References 40 publications

Bibo Stabilisation of Continuous–Time Takagi–Sugeno Systems under Persistent Perturbations and Input Saturation

Bibo Stabilisation of Continuous–Time Takagi–Sugeno Systems under Persistent Perturbations and Input Saturation

Robust H_∞ static output‐feedback control for discrete‐time fuzzy systems with actuator saturation via fuzzy Lyapunov functions

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

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

Cited by 5 publications

References 40 publications

Bibo Stabilisation of Continuous–Time Takagi–Sugeno Systems under Persistent Perturbations and Input Saturation

Bibo Stabilisation of Continuous–Time Takagi–Sugeno Systems under Persistent Perturbations and Input Saturation

Robust H∞ static output‐feedback control for discrete‐time fuzzy systems with actuator saturation via fuzzy Lyapunov functions

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

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

Robust H_∞ static output‐feedback control for discrete‐time fuzzy systems with actuator saturation via fuzzy Lyapunov functions