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

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

International Journal of Applied Mathematics and Computer Science (2016)

  • Volume: 26, Issue: 1, page 133-145
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Ruirui Duan, et al. "Stability analysis and $H_{∞}$ control of discrete T-S fuzzy hyperbolic systems." International Journal of Applied Mathematics and Computer Science 26.1 (2016): 133-145. <http://eudml.org/doc/276442>.

@article{RuiruiDuan2016,
abstract = {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.},
author = {Ruirui Duan, Junmin Li, Yanni Zhang, Ying Yang, Guopei Chen},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {discrete T-S fuzzy hyperbolic model; parallel distributed compensation (PDC); positive diagonally dominant (PDD) matrices; robust stability},
language = {eng},
number = {1},
pages = {133-145},
title = {Stability analysis and $H_\{∞\}$ control of discrete T-S fuzzy hyperbolic systems},
url = {http://eudml.org/doc/276442},
volume = {26},
year = {2016},
}

TY - JOUR
AU - Ruirui Duan
AU - Junmin Li
AU - Yanni Zhang
AU - Ying Yang
AU - Guopei Chen
TI - Stability analysis and $H_{∞}$ control of discrete T-S fuzzy hyperbolic systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2016
VL - 26
IS - 1
SP - 133
EP - 145
AB - 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.
LA - eng
KW - discrete T-S fuzzy hyperbolic model; parallel distributed compensation (PDC); positive diagonally dominant (PDD) matrices; robust stability
UR - http://eudml.org/doc/276442
ER -

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