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<p>In this paper, the authors propose an approach to properly aggregate a reversible discrete-time switched linear system and prove that, for any <i>n</i>-dimensional exponentially stabilizable switched system, the authors could design up to <i>n</i> linear gain matrices, such that the extended system is also exponentially stabilizable as a switched autonomous system. By utilizing the pathwise state feedback switching strategy of the switched autonomous system, the original system is aggregated into a piecewise linear system that is step-wise norm contractive and exponentially stable. The authors also develop a robust switching design mechanism that simultaneously achieves exponential stability, structural stability, and input-to-state stability for the closed-loop system. A numerical example is presented to demonstrate the effectiveness of the proposed design scheme.</p>

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Aggregation and Robustness of Reversible Switched Linear Systems

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Xuehui Li,
  • Zhou Zheng,
  • Hairong Dong,
  • Zhendong Sun

摘要

In this paper, the authors propose an approach to properly aggregate a reversible discrete-time switched linear system and prove that, for any n-dimensional exponentially stabilizable switched system, the authors could design up to n linear gain matrices, such that the extended system is also exponentially stabilizable as a switched autonomous system. By utilizing the pathwise state feedback switching strategy of the switched autonomous system, the original system is aggregated into a piecewise linear system that is step-wise norm contractive and exponentially stable. The authors also develop a robust switching design mechanism that simultaneously achieves exponential stability, structural stability, and input-to-state stability for the closed-loop system. A numerical example is presented to demonstrate the effectiveness of the proposed design scheme.