Stabilization of discrete-time positive switched T-S fuzzy systems subject to actuator saturation

Gengjiao Yang; Fei Hao; Lin Zhang; Lixin Gao; Gengjiao Yang; Fei Hao; Lin Zhang; Lixin Gao

doi:10.3934/math.2023640

AIMS Mathematics

2023, Volume 8, Issue 6: 12708-12728. doi: 10.3934/math.2023640

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Stabilization of discrete-time positive switched T-S fuzzy systems subject to actuator saturation

1.
College of Mathematics and Physics, Wenzhou University, Wenzhou, Zhejiang 325035, China
2.
School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China

Received: 24 January 2023 Revised: 17 March 2023 Accepted: 21 March 2023 Published: 29 March 2023

The stabilization of discrete-time positive switched Takagi-Sugeno (T-S) fuzzy systems with actuator saturation is investigated in this paper. It is assumed that the switched subsystems are partially stabilizable. Based on the convex hull technique (CHT) and parallel distribution compensation (PDC) algorithm, a saturated fuzzy controller and slow-fast combined mode-dependent average dwell time (MDADT) switching signal are co-designed and sufficient conditions for the positivity and stability of closed-loop positive switched T-S fuzzy systems (PSTSFSs) are developed, which can be reduced to the ones under the case where all switched subsystems are stabilizable. Moreover, the largest attraction domain estimation (ADE) is given for PSTSFSs by formulating an optimization problem. Finally, the designed control scheme is applied to two illustrative examples to verify its availability and superiority.
- stabilization,
- actuator saturation,
- positive systems,
- switched systems,
- T-S fuzzy systems
Citation: Gengjiao Yang, Fei Hao, Lin Zhang, Lixin Gao. Stabilization of discrete-time positive switched T-S fuzzy systems subject to actuator saturation[J]. AIMS Mathematics, 2023, 8(6): 12708-12728. doi: 10.3934/math.2023640

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Abstract

The stabilization of discrete-time positive switched Takagi-Sugeno (T-S) fuzzy systems with actuator saturation is investigated in this paper. It is assumed that the switched subsystems are partially stabilizable. Based on the convex hull technique (CHT) and parallel distribution compensation (PDC) algorithm, a saturated fuzzy controller and slow-fast combined mode-dependent average dwell time (MDADT) switching signal are co-designed and sufficient conditions for the positivity and stability of closed-loop positive switched T-S fuzzy systems (PSTSFSs) are developed, which can be reduced to the ones under the case where all switched subsystems are stabilizable. Moreover, the largest attraction domain estimation (ADE) is given for PSTSFSs by formulating an optimization problem. Finally, the designed control scheme is applied to two illustrative examples to verify its availability and superiority.

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