Further results on robust fuzzy dynamic systems with LMI 𝓓-stability constraints

Wudhichai Assawinchaichote

International Journal of Applied Mathematics and Computer Science (2014)

  • Volume: 24, Issue: 4, page 785-794
  • ISSN: 1641-876X

Abstract

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This paper examines the problem of designing a robust ∞ fuzzy controller with -stability constraints for a class of nonlinear dynamic systems which is described by a Takagi-Sugeno (TS) fuzzy model. Fuzzy modelling is a multi-model approach in which simple sub-models are combined to determine the global behavior of the system. Based on a linear matrix inequality (LMI) approach, we develop a robust ∞ fuzzy controller that guarantees (i) the ₂-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, and (ii) the closed-loop poles of each local system to be within a specified stability region. Sufficient conditions for the controller are given in terms of LMIs. Finally, to show the effectiveness of the designed approach, an example is provided to illustrate the use of the proposed methodology.

How to cite

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Wudhichai Assawinchaichote. "Further results on robust fuzzy dynamic systems with LMI 𝓓-stability constraints." International Journal of Applied Mathematics and Computer Science 24.4 (2014): 785-794. <http://eudml.org/doc/271870>.

@article{WudhichaiAssawinchaichote2014,
abstract = {This paper examines the problem of designing a robust $_∞$ fuzzy controller with -stability constraints for a class of nonlinear dynamic systems which is described by a Takagi-Sugeno (TS) fuzzy model. Fuzzy modelling is a multi-model approach in which simple sub-models are combined to determine the global behavior of the system. Based on a linear matrix inequality (LMI) approach, we develop a robust $_∞$ fuzzy controller that guarantees (i) the ₂-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, and (ii) the closed-loop poles of each local system to be within a specified stability region. Sufficient conditions for the controller are given in terms of LMIs. Finally, to show the effectiveness of the designed approach, an example is provided to illustrate the use of the proposed methodology.},
author = {Wudhichai Assawinchaichote},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {fuzzy controller; robust $_∞$ control; LMI approach; 𝓓-stability; Takagi-Sugeno fuzzy model; robust control; D-stability},
language = {eng},
number = {4},
pages = {785-794},
title = {Further results on robust fuzzy dynamic systems with LMI 𝓓-stability constraints},
url = {http://eudml.org/doc/271870},
volume = {24},
year = {2014},
}

TY - JOUR
AU - Wudhichai Assawinchaichote
TI - Further results on robust fuzzy dynamic systems with LMI 𝓓-stability constraints
JO - International Journal of Applied Mathematics and Computer Science
PY - 2014
VL - 24
IS - 4
SP - 785
EP - 794
AB - This paper examines the problem of designing a robust $_∞$ fuzzy controller with -stability constraints for a class of nonlinear dynamic systems which is described by a Takagi-Sugeno (TS) fuzzy model. Fuzzy modelling is a multi-model approach in which simple sub-models are combined to determine the global behavior of the system. Based on a linear matrix inequality (LMI) approach, we develop a robust $_∞$ fuzzy controller that guarantees (i) the ₂-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, and (ii) the closed-loop poles of each local system to be within a specified stability region. Sufficient conditions for the controller are given in terms of LMIs. Finally, to show the effectiveness of the designed approach, an example is provided to illustrate the use of the proposed methodology.
LA - eng
KW - fuzzy controller; robust $_∞$ control; LMI approach; 𝓓-stability; Takagi-Sugeno fuzzy model; robust control; D-stability
UR - http://eudml.org/doc/271870
ER -

References

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