Lyapunov Conditions for Input-to-State Stability of Hybrid Systems with Memory

TL;DR

This paper develops Lyapunov-based conditions to ensure input-to-state stability in hybrid systems with memory, accounting for time delays and providing extensions for special cases.

Contribution

It introduces new Lyapunov-Razumikhin and Lyapunov-Krasovskii conditions for hybrid systems with memory, including relaxations for non-strict decrease scenarios.

Findings

Lyapunov conditions guarantee input-to-state stability.

Extensions cover stable flow/jump cases.

Illustrative examples validate the theoretical results.

Abstract

This paper studies input-to-state stability for hybrid systems with memory, which models hybrid dynamics affected by time delays. Using both Lyapunov-Razumikhin functions and Lyapunov-Krasovskii functionals, Lyapunov-based sufficient conditions are established for input-to-state stability. In addition, further extensions and relaxations are proposed for special cases, such as the stable flow/jump cases and the cases that Lyapunov functions do not decrease strictly during flow/jumps. Finally, two examples are used to illustrate the developed results.