Switching robustness analysis for switched linear systems

This paper investigates the stability of switched linear systems with the perturbed switching. In premises of introducing the notions of common child-path and parent-path, we define distance between switching paths. A constructive procedure is proposed for finding common child-paths, then we reveal a relationship between common child-path and parent-path, and subsequently formulate the distance. Finally, distance between switching paths is extended to relative distance between switching signals, which is used to analyze the robustness for a class of switched linear systems.