TY - JOUR
T1 - Dynamical Analysis of T–S Fuzzy Financial Systems
T2 - A Sampled-Data Control Approach
AU - Thangavel, Bhagyaraj
AU - Srinivasan, Sabarathinam
AU - Kathamuthu, Thamilmaran
AU - Zhai, Guisheng
AU - Gunasekaran, Nallappan
N1 - Funding Information:
We thank Dr. A. Ishaq Ahamed for their valuable comments and suggestions. T. Kathamuthu acknowledges the financial support of the Department of Science and Technology (DST)-PURSE PHASE-II, Government of India, under PURSE scheme. S. Srinivasan acknowledges the Basic Research Program of the National Research University, Higher School of Economics, Moscow. The authors would like to thank Shibaura Institute of Technology and Toyota Technological Institute, Japan, for the financial aid to support this research.
Publisher Copyright:
© 2022, The Author(s) under exclusive licence to Taiwan Fuzzy Systems Association.
PY - 2022/6
Y1 - 2022/6
N2 - This paper investigates the sampled-data stabilization of the Takagi–Sugano (T–S) fuzzy system, focusing on the existence of extreme event (EE) and its application to the financial model. The mathematical model of finance system is constructed through real time hardware experiment for the first time. The EE is identified in certain ranges of system parameters, is characterized and confirmed through numerical, analytical and experimental investigations. The stability analysis confirms that the EE occurs via an interior crisis phenomenon. The dynamical system is identified through bifurcation analysis and its corresponding Lyapunov exponent. The second phase of the manuscript is that, by building an appropriate Lyapunov function, sufficient conditions are derived to guarantee that the addressed T–S fuzzy financial system is asymptotically stable. The proposed stability conditions are expressed in terms of linear matrix inequalities (LMIs). In addition, the sampled-data control techniques are used to stabilize the EE. Finally, the simulation result is presented to support the proposed control scheme.
AB - This paper investigates the sampled-data stabilization of the Takagi–Sugano (T–S) fuzzy system, focusing on the existence of extreme event (EE) and its application to the financial model. The mathematical model of finance system is constructed through real time hardware experiment for the first time. The EE is identified in certain ranges of system parameters, is characterized and confirmed through numerical, analytical and experimental investigations. The stability analysis confirms that the EE occurs via an interior crisis phenomenon. The dynamical system is identified through bifurcation analysis and its corresponding Lyapunov exponent. The second phase of the manuscript is that, by building an appropriate Lyapunov function, sufficient conditions are derived to guarantee that the addressed T–S fuzzy financial system is asymptotically stable. The proposed stability conditions are expressed in terms of linear matrix inequalities (LMIs). In addition, the sampled-data control techniques are used to stabilize the EE. Finally, the simulation result is presented to support the proposed control scheme.
KW - Extreme event
KW - Hamilton–Jacobi inequality
KW - Linear matrix inequality
KW - Lyapunov spectra
KW - Sampled-data control
KW - T–S fuzzy method
UR - http://www.scopus.com/inward/record.url?scp=85124978246&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85124978246&partnerID=8YFLogxK
U2 - 10.1007/s40815-022-01249-4
DO - 10.1007/s40815-022-01249-4
M3 - Article
AN - SCOPUS:85124978246
SN - 1562-2479
VL - 24
SP - 1944
EP - 1957
JO - International Journal of Fuzzy Systems
JF - International Journal of Fuzzy Systems
IS - 4
ER -