Improved time-varying Halanay inequality with impulses and its application to stability analysis of time-varying semi-Markov switched systems with time-delays

We propose an improved time-varying Halanay inequality with impulses. This Halanay inequality can be applied to indefinite multiple Lyapunov functions to handle the interactions between subsystems caused by time delays. Based on this theoretical framework, we establish almost sure stability criteria for time-varying semi-Markov switched systems with time delays. Numerical examples demonstrate the effectiveness and advantages of the proposed results.