# A note on uniform exponential stability of linear periodic time-varying systems

## TL;DR

This paper introduces new criteria for assessing the uniform exponential stability of linear periodic time-varying systems, using logarithmic norms and bounds on Floquet exponents, and examines robustness under disturbances.

## Contribution

It presents novel stability criteria based on logarithmic norms and provides bounds for Floquet exponents, enhancing analysis of periodic systems.

## Key findings

- New stability criteria derived using logarithmic norms
- Bounds established for Floquet characteristic exponents
- Robustness analysis under external disturbances

## Abstract

In this paper we derive new criterion for uniform stability assessment of the linear periodic time-varying systems $\dot x=A(t)x,$ $A(t+T)=A(t).$ As a corollary, the lower and upper bounds for the Floquet characteristic exponents are established. The approach is based on the use of logarithmic norm of the system matrix $A(t).$ Finally we analyze the robustness of the stability property under external disturbance.