Stability Analysis of a Type of Takagi-Sugeno PI Fuzzy Control Systems Using Circle Criterion

DOI

10.2991/ijcis.2011.4.2.8How to use a DOI?

Keywords

fuzzy control systems, Takagi-Sugeno (T-S) PI fuzzy controllers, stability analysis, circle criterion, frequency response methods.

Abstract

A type of Takagi-Sugeno (T-S) Proportional-Integral (PI) fuzzy controllers is studied. The T-S PI fuzzy controller is formed by a T-S Proportional-Derivative (PD) fuzzy controller connected with an integrator. In this particular structure, the T-S PD fuzzy controller is a weighted sum of some linear PD sub-controllers. The mathematical properties of our T-S PI fuzzy controller are also investigated. Based on these properties, the global asymptotic stability of the fuzzy control systems, in which the T-S PI fuzzy controllers are employed, are analyzed by using the well-known circle criterion. A sufficient condition with an elegant graphical interpretation in the frequency domain is further derived to guarantee the global asymptotic stability of the above fuzzy control systems. Finally, two numerical examples are provided to demonstrate how to deploy this method in analyzing the T-S PI fuzzy control systems in the frequency domain with the aid of some simple graphs.

Copyright

© 2011, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Kairui Cao
AU  - X.Z. Gao
AU  - Xianlin Huang
AU  - Xiaojun Ban
PY  - 2011
DA  - 2011/04/01
TI  - Stability Analysis of a Type of Takagi-Sugeno PI Fuzzy Control Systems Using Circle Criterion
JO  - International Journal of Computational Intelligence Systems
SP  - 196
EP  - 207
VL  - 4
IS  - 2
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.2011.4.2.8
DO  - 10.2991/ijcis.2011.4.2.8
ID  - Cao2011
ER  -