A new fuzzy Lyapunov approach to non-quadratic stabilization of Takagi-Sugeno fuzzy models

Ibtissem Abdelmalek; Noureddine Goléa; Mohamed Hadjili

International Journal of Applied Mathematics and Computer Science (2007)

  • Volume: 17, Issue: 1, page 39-51
  • ISSN: 1641-876X

Abstract

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In this paper, new non-quadratic stability conditions are derived based on the parallel distributed compensation scheme to stabilize Takagi-Sugeno (T-S) fuzzy systems. We use a non-quadratic Lyapunov function as a fuzzy mixture of multiple quadratic Lyapunov functions. The quadratic Lyapunov functions share the same membership functions with the T-S fuzzy model. The stability conditions we propose are less conservative and stabilize also fuzzy systems which do not admit a quadratic stabilization. The proposed approach is based on two assumptions. The first one relates to a proportional relation between multiple Lyapunov functions and the second one considers an upper bound to the time derivative of the premise membership functions. To illustrate the advantages of our proposal, four examples are given.

How to cite

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Abdelmalek, Ibtissem, Goléa, Noureddine, and Hadjili, Mohamed. "A new fuzzy Lyapunov approach to non-quadratic stabilization of Takagi-Sugeno fuzzy models." International Journal of Applied Mathematics and Computer Science 17.1 (2007): 39-51. <http://eudml.org/doc/207820>.

@article{Abdelmalek2007,
abstract = {In this paper, new non-quadratic stability conditions are derived based on the parallel distributed compensation scheme to stabilize Takagi-Sugeno (T-S) fuzzy systems. We use a non-quadratic Lyapunov function as a fuzzy mixture of multiple quadratic Lyapunov functions. The quadratic Lyapunov functions share the same membership functions with the T-S fuzzy model. The stability conditions we propose are less conservative and stabilize also fuzzy systems which do not admit a quadratic stabilization. The proposed approach is based on two assumptions. The first one relates to a proportional relation between multiple Lyapunov functions and the second one considers an upper bound to the time derivative of the premise membership functions. To illustrate the advantages of our proposal, four examples are given.},
author = {Abdelmalek, Ibtissem, Goléa, Noureddine, Hadjili, Mohamed},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {linear matrix inequalities; non-quadratic stability conditions; T-S fuzzy systems; stabilization; parallel distributed compensation},
language = {eng},
number = {1},
pages = {39-51},
title = {A new fuzzy Lyapunov approach to non-quadratic stabilization of Takagi-Sugeno fuzzy models},
url = {http://eudml.org/doc/207820},
volume = {17},
year = {2007},
}

TY - JOUR
AU - Abdelmalek, Ibtissem
AU - Goléa, Noureddine
AU - Hadjili, Mohamed
TI - A new fuzzy Lyapunov approach to non-quadratic stabilization of Takagi-Sugeno fuzzy models
JO - International Journal of Applied Mathematics and Computer Science
PY - 2007
VL - 17
IS - 1
SP - 39
EP - 51
AB - In this paper, new non-quadratic stability conditions are derived based on the parallel distributed compensation scheme to stabilize Takagi-Sugeno (T-S) fuzzy systems. We use a non-quadratic Lyapunov function as a fuzzy mixture of multiple quadratic Lyapunov functions. The quadratic Lyapunov functions share the same membership functions with the T-S fuzzy model. The stability conditions we propose are less conservative and stabilize also fuzzy systems which do not admit a quadratic stabilization. The proposed approach is based on two assumptions. The first one relates to a proportional relation between multiple Lyapunov functions and the second one considers an upper bound to the time derivative of the premise membership functions. To illustrate the advantages of our proposal, four examples are given.
LA - eng
KW - linear matrix inequalities; non-quadratic stability conditions; T-S fuzzy systems; stabilization; parallel distributed compensation
UR - http://eudml.org/doc/207820
ER -

References

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