Stability analysis of switching systems with all modes unstable based on a $ \Phi $-dependent max-minimum dwell time method

Qiang Yu; Yuanyang Feng; Qiang Yu; Yuanyang Feng

doi:10.3934/math.2024236

AIMS Mathematics

2024, Volume 9, Issue 2: 4863-4881. doi: 10.3934/math.2024236

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Stability analysis of switching systems with all modes unstable based on a $ \Phi $-dependent max-minimum dwell time method

Qiang Yu ^,,
Yuanyang Feng

School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan 030032, China

Received: 27 November 2023 Revised: 05 January 2024 Accepted: 08 January 2024 Published: 23 January 2024
MSC : 34D20, 93D15

This paper applies stable and unstable switching instants to study switching systems with unstable modes under time-dependent switching signals. A new Lyapunov function is proposed to study the properties of switching instant using different $ \Phi $-dependent max-minimum dwell time methods. After that, the global exponential stability conditions for nonlinear and linear switching systems are derived and stable switching is used to compensate for unstable switching and unstable modes. The relevant results are extended to the controller design of linear switching systems. Finally, a simulation verifies the effectiveness of the results of this paper.
- switching systems,
- stable and unstable subsystems,
- $ \Phi $-dependent max-minimum dwell time,
- Lyapunov function,
- globally exponentially stable
Citation: Qiang Yu, Yuanyang Feng. Stability analysis of switching systems with all modes unstable based on a $ \Phi $-dependent max-minimum dwell time method[J]. AIMS Mathematics, 2024, 9(2): 4863-4881. doi: 10.3934/math.2024236

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Abstract

This paper applies stable and unstable switching instants to study switching systems with unstable modes under time-dependent switching signals. A new Lyapunov function is proposed to study the properties of switching instant using different $ \Phi $-dependent max-minimum dwell time methods. After that, the global exponential stability conditions for nonlinear and linear switching systems are derived and stable switching is used to compensate for unstable switching and unstable modes. The relevant results are extended to the controller design of linear switching systems. Finally, a simulation verifies the effectiveness of the results of this paper.

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