Stabilization of 2-D discrete-time switched positive linear systems via weak switched linear copositive Lyapunov function

Mengying Sun; Dadong Tian; Yongping Zhang; Mengying Sun; Dadong Tian; Yongping Zhang

doi:10.3934/mmc.2026018

Mathematical Modelling and Control

2026, Volume 6, Issue 3: 240-251. doi: 10.3934/mmc.2026018

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Research article

Stabilization of 2-D discrete-time switched positive linear systems via weak switched linear copositive Lyapunov function

1.
School of Mathematics and Statistics, Shandong University, Weihai 264209, China
2.
College of Information Science and Engineering, Shandong Agricultural University, Taian 271018, China

Received: 25 September 2024 Revised: 26 May 2025 Accepted: 04 September 2025 Published: 27 August 2026

In this paper, we study the stabilization problem of 2-D discrete-time switched positive linear systems. First, by using the common linear copositive Lyapunov function, it is showed that the 2-D switched positive linear system is asymptotically stable under arbitrary switching. Then, a weak common linear copositive Lyapunov function is introduced. By designing new time-dependent switching signals, the asymptotic stability of the 2-D system with disturbance is demonstrated. Finally, a function with a wider range of adaptation - weak switched linear copositive Lyapunov function is considered, and the asymptotic stability of the corresponding system under a given switching signal is proved. A numerical example demonstrates the effectiveness of the obtained results.
- 2-D discrete-time switched positive linear systems,
- stabilization,
- switching signal,
- weak switched linear copositive Lyapunov function
Citation: Mengying Sun, Dadong Tian, Yongping Zhang. Stabilization of 2-D discrete-time switched positive linear systems via weak switched linear copositive Lyapunov function[J]. Mathematical Modelling and Control, 2026, 6(3): 240-251. doi: 10.3934/mmc.2026018

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Abstract

In this paper, we study the stabilization problem of 2-D discrete-time switched positive linear systems. First, by using the common linear copositive Lyapunov function, it is showed that the 2-D switched positive linear system is asymptotically stable under arbitrary switching. Then, a weak common linear copositive Lyapunov function is introduced. By designing new time-dependent switching signals, the asymptotic stability of the 2-D system with disturbance is demonstrated. Finally, a function with a wider range of adaptation - weak switched linear copositive Lyapunov function is considered, and the asymptotic stability of the corresponding system under a given switching signal is proved. A numerical example demonstrates the effectiveness of the obtained results.

References

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