# Finite-Time Stability of Hybrid Systems: A Multiple Generalized Lyapunov Functions Approach

## TL;DR

This paper introduces a less conservative method for ensuring finite-time stability in hybrid systems using multiple generalized Lyapunov functions that can increase during flows and jumps, broadening applicability.

## Contribution

It proposes a novel approach allowing Lyapunov functions to increase, expanding the class of hybrid systems for which finite-time stability can be guaranteed.

## Key findings

- Finite-time stability can be achieved even with increasing Lyapunov functions.
- The method is less conservative than previous approaches.
- Numerical example confirms the effectiveness of the proposed approach.

## Abstract

This paper studies finite-time stability of a class of hybrid systems. We present sufficient conditions in terms of multiple generalized Lyapunov functions for the origin of the hybrid system to be finite-time stable. More specifically, we show that even if the value of the generalized Lyapunov functions increase between consecutive switches, finite-time stability can be guaranteed if the finite-time convergent mode is active long enough. In contrast to earlier work where the Lyapunov functions are required to be decreasing during the continuous flows and non-increasing at the discrete jumps, we allow the generalized Lyapunov functions to increase \emph{both} during the continuous flows and the discrete jumps. As thus, the derived stability results are less conservative compared to the related literature. Numerical example demonstrates the efficacy of the proposed methods.