Robust stability of switched interconnected systems with multiple time delays and switching uncertainties

Huanbin Xue; Xiaopeng Yang; Huanbin Xue; Xiaopeng Yang

doi:10.3934/math.2025820

AIMS Mathematics

2025, Volume 10, Issue 8: 18356-18380. doi: 10.3934/math.2025820

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Research article

Robust stability of switched interconnected systems with multiple time delays and switching uncertainties

Huanbin Xue ,
Xiaopeng Yang ^,

School of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, China

Received: 23 April 2025 Revised: 21 June 2025 Accepted: 25 July 2025 Published: 13 August 2025
MSC : 34D20

This study investigates the problem of robust stability in a class of switched interconnected systems that involve unstable modes, time-varying and continuously distributed state delays, as well as uncertainties in switching signal and system parameters. Switching uncertainties lead to fluctuations in both the prescribed switching instants and the nominal switching sequence, which significantly affect system stability. To address these challenges, two novel concepts are introduced: the composite switching signal and the generalized nominal switching signal. Additionally, a new index, referred to as the generalized mode-changing rate, is proposed. By utilizing these concepts and the new index, the average dwell time approach and the vector Lyapunov function method are integrated to derive sufficient conditions for ensuring the robust exponential stability of the system. Finally, a numerical example is provided to illustrate the effectiveness and applicability of the proposed theory.
- robust stability,
- switched system,
- switching uncertainties,
- unstable modes,
- unbounded delay
Citation: Huanbin Xue, Xiaopeng Yang. Robust stability of switched interconnected systems with multiple time delays and switching uncertainties[J]. AIMS Mathematics, 2025, 10(8): 18356-18380. doi: 10.3934/math.2025820

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Abstract

This study investigates the problem of robust stability in a class of switched interconnected systems that involve unstable modes, time-varying and continuously distributed state delays, as well as uncertainties in switching signal and system parameters. Switching uncertainties lead to fluctuations in both the prescribed switching instants and the nominal switching sequence, which significantly affect system stability. To address these challenges, two novel concepts are introduced: the composite switching signal and the generalized nominal switching signal. Additionally, a new index, referred to as the generalized mode-changing rate, is proposed. By utilizing these concepts and the new index, the average dwell time approach and the vector Lyapunov function method are integrated to derive sufficient conditions for ensuring the robust exponential stability of the system. Finally, a numerical example is provided to illustrate the effectiveness and applicability of the proposed theory.

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