This paper investigates the global exponential stability of discrete-time impulsive switched systems with dimensional switching, where subsystems operate in different state dimensions and impulse effects occur during transitions. A modified global exponential stability theorem is developed using an improved Lyapunov analysis approach that incorporates a flexible design parameter \(\epsilon \) . This parameter enables systematic balancing between system dynamics sensitivity and impulse effect influence, providing enhanced design flexibility. The theoretical framework employs mode-dependent Lyapunov functions and applies the generalized Cauchy-Schwarz inequality to analyze the combined effects of state evolution and impulse inputs. The main result establishes a modified average dwell time condition that guarantees global exponential stability, with parameter \(\epsilon \) allowing for system-specific optimization. The theoretical findings are validated through a numerical example involving three subsystems with dimensions 2, 3, and 2, respectively, demonstrating stable convergence despite dimensional transitions and impulse inputs. The proposed approach offers improved stability analysis capabilities for complex switched systems.

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Global Exponential Stability of Multi-dimensional Discrete-Time Switched Systems

  • Xinbao Li,
  • Yan Zhang,
  • Ronghao Wang,
  • Shuo Li,
  • Zhengrong Xiang

摘要

This paper investigates the global exponential stability of discrete-time impulsive switched systems with dimensional switching, where subsystems operate in different state dimensions and impulse effects occur during transitions. A modified global exponential stability theorem is developed using an improved Lyapunov analysis approach that incorporates a flexible design parameter \(\epsilon \) . This parameter enables systematic balancing between system dynamics sensitivity and impulse effect influence, providing enhanced design flexibility. The theoretical framework employs mode-dependent Lyapunov functions and applies the generalized Cauchy-Schwarz inequality to analyze the combined effects of state evolution and impulse inputs. The main result establishes a modified average dwell time condition that guarantees global exponential stability, with parameter \(\epsilon \) allowing for system-specific optimization. The theoretical findings are validated through a numerical example involving three subsystems with dimensions 2, 3, and 2, respectively, demonstrating stable convergence despite dimensional transitions and impulse inputs. The proposed approach offers improved stability analysis capabilities for complex switched systems.