An improved finite-time stabilization of discontinuous non-autonomous IT2 T-S fuzzy interconnected complex-valued systems: A fuzzy switching state-feedback control method

Xiong Jian; Zengyun Wang; Aitong Xin; Yujing Chen; Shujuan Xie; Xiong Jian; Zengyun Wang; Aitong Xin; Yujing Chen; Shujuan Xie

doi:10.3934/era.2023014

Electronic Research Archive

2023, Volume 31, Issue 1: 273-298. doi: 10.3934/era.2023014

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An improved finite-time stabilization of discontinuous non-autonomous IT2 T-S fuzzy interconnected complex-valued systems: A fuzzy switching state-feedback control method

1.
School of Mathematics and Statistics, Hunan First Normal University, Changsha 410205, China
2.
School of Computer Science, Hunan First Normal University, Changsha 410205, China

Received: 05 August 2022 Revised: 09 October 2022 Accepted: 20 October 2022 Published: 31 October 2022

Based on the type-2 Takagi-Sugeno (IT2 T-S) fuzzy theory, a non-autonomous fuzzy complex-valued dynamical system with discontinuous interconnection function is formulated. Under the framework of Filippov, the finite-time stabilization (FTS) problem is investigated by using an indefinite-derivative Lyapunov function method, where the derivative of the constructed Lyapunov function is allowed to be positive. By designing a fuzzy switching state feedback controller involving time-varying control gain parameters, several sufficient criteria are established to determine the considered system's stability in finite time. Correspondingly, due to the time-varying system parameters and the designed time-dependent control gain coefficients, a more flexible settling time (ST) is estimated. Finally, an example is presented to confirm the proposed methodology.
Citation: Xiong Jian, Zengyun Wang, Aitong Xin, Yujing Chen, Shujuan Xie. An improved finite-time stabilization of discontinuous non-autonomous IT2 T-S fuzzy interconnected complex-valued systems: A fuzzy switching state-feedback control method[J]. Electronic Research Archive, 2023, 31(1): 273-298. doi: 10.3934/era.2023014

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Abstract

Based on the type-2 Takagi-Sugeno (IT2 T-S) fuzzy theory, a non-autonomous fuzzy complex-valued dynamical system with discontinuous interconnection function is formulated. Under the framework of Filippov, the finite-time stabilization (FTS) problem is investigated by using an indefinite-derivative Lyapunov function method, where the derivative of the constructed Lyapunov function is allowed to be positive. By designing a fuzzy switching state feedback controller involving time-varying control gain parameters, several sufficient criteria are established to determine the considered system's stability in finite time. Correspondingly, due to the time-varying system parameters and the designed time-dependent control gain coefficients, a more flexible settling time (ST) is estimated. Finally, an example is presented to confirm the proposed methodology.

References

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