Unified stability criteria for impulsive switched T-S fuzzy systems with time delays under the bounded admissible edge-dependent average dwell time

Suzhen Ran; Suzhen Ran

doi:10.3934/math.2026767

AIMS Mathematics

2026, Volume 11, Issue 6: 18845-18868. doi: 10.3934/math.2026767

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Research article

Unified stability criteria for impulsive switched T-S fuzzy systems with time delays under the bounded admissible edge-dependent average dwell time

Suzhen Ran ^,

School of Foundation Studies, Zhejiang Pharmaceutical University, Ningbo 315500, China

Received: 20 April 2026 Revised: 10 June 2026 Accepted: 15 June 2026 Published: 26 June 2026
MSC : 93C30, 93C42

This paper is concerned with the input-to-state stability (ISS) problem for a class of impulsive switched nonlinear systems with time delays. By utilising the Takagi-Sugeno (T-S) fuzzy method, the subsystems and impulses are designed for different fuzzy rules and membership functions, which can increase the degree of freedom and flexibility of designing. Moreover, based on admissible edge-dependent average dwell time (AED-ADT) and mode-dependent bounded maximum average dwell time (MD-BMADT), we establish a unified bounded admissible edge-dependent average dwell time (BAED-ADT) criterion for nonlinear systems. Then, the ISS property is also derived for impulsive switched T-S fuzzy systems when the system is with all stable, some unstable, and all unstable subsystems. Meanwhile, the slow and fast switching methods are used for stable or unstable subsystems. By employing the new BAED-ADT method and admissible edge-dependent average impulsive interval (AED-AII) technique, some new sufficient criteria of a "unified" ISS for impulsive switched systems are derived by constructing the time-scheduled multiple Lyapunov functions. Finally, several illustrative examples are provided to illustrate our results.
Citation: Suzhen Ran. Unified stability criteria for impulsive switched T-S fuzzy systems with time delays under the bounded admissible edge-dependent average dwell time[J]. AIMS Mathematics, 2026, 11(6): 18845-18868. doi: 10.3934/math.2026767

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Abstract

This paper is concerned with the input-to-state stability (ISS) problem for a class of impulsive switched nonlinear systems with time delays. By utilising the Takagi-Sugeno (T-S) fuzzy method, the subsystems and impulses are designed for different fuzzy rules and membership functions, which can increase the degree of freedom and flexibility of designing. Moreover, based on admissible edge-dependent average dwell time (AED-ADT) and mode-dependent bounded maximum average dwell time (MD-BMADT), we establish a unified bounded admissible edge-dependent average dwell time (BAED-ADT) criterion for nonlinear systems. Then, the ISS property is also derived for impulsive switched T-S fuzzy systems when the system is with all stable, some unstable, and all unstable subsystems. Meanwhile, the slow and fast switching methods are used for stable or unstable subsystems. By employing the new BAED-ADT method and admissible edge-dependent average impulsive interval (AED-AII) technique, some new sufficient criteria of a "unified" ISS for impulsive switched systems are derived by constructing the time-scheduled multiple Lyapunov functions. Finally, several illustrative examples are provided to illustrate our results.

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