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Dynamical Analysis of T–S Fuzzy Financial Systems: A Sampled-Data Control Approach

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Abstract

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.

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Acknowledgements

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.

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Authors and Affiliations

  1. Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli, Tamil Nadu, India

    Bhagyaraj Thangavel & Thamilmaran Kathamuthu

  2. Laboratory of Complex Systems Modelling and Control, Faculty of Computer Science, National Research University, High School of Economics, Moscow, Russia

    Sabarathinam Srinivasan

  3. Department of Mathematical Sciences, Shibaura Institute of Technology, Saitama, 337-8570, Japan

    Guisheng Zhai

  4. Computational Intelligence Laboratory, Toyota Technological Institute, Nagoya, 468-8511, Japan

    Nallappan Gunasekaran

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  1. Bhagyaraj Thangavel
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Correspondence to Guisheng Zhai.

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Thangavel, B., Srinivasan, S., Kathamuthu, T. et al. Dynamical Analysis of T–S Fuzzy Financial Systems: A Sampled-Data Control Approach. Int. J. Fuzzy Syst. 24, 1944–1957 (2022). https://doi.org/10.1007/s40815-022-01249-4

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  • DOI: https://doi.org/10.1007/s40815-022-01249-4

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