Stability conditions for impulsive dynamical systems

In this work, we consider impulsive dynamical systems evolving on an infinite-dimensional space and subjected to external perturbations. We look for stability conditions that guarantee the input-to-state stability for such systems. Our new dwell-time conditions allow the situation, where both continuous and discrete dynamics can be unstable simultaneously. Lyapunov like methods are developed for this purpose. Illustrative finite and infinite dimensional examples are provided to demonstrate the application of the main results. These examples cannot be treated by any other published approach and demonstrate the effectiveness of our results.

Automated summary

This work investigates the stability conditions of impulsive dynamical systems evolving on an infinite-dimensional space and under external perturbations. New dwell-time conditions are proposed to handle situations where both continuous and discrete dynamics can be unstable simultaneously, with Lyapunov-like methods developed for this purpose. Finite and infinite dimensional examples are provided to demonstrate the application and effectiveness of the main results, which cannot be addressed by any other existing approaches.