Datko-Pazy conditions for nonuniform exponential stability

TL;DR

This paper establishes Datko-Pazy type conditions for linear cocycles that ensure all Lyapunov exponents are negative, and introduces new criteria for uniform exponential stability by integrating subadditive ergodic optimization techniques.

Contribution

It provides novel criteria linking Datko-Pazy conditions to the negativity of Lyapunov exponents and uniform exponential stability for linear cocycles.

Findings

All Lyapunov exponents are negative under certain conditions.

New criteria for uniform exponential stability are derived.

Results apply to cocycles over maps and flows.

Abstract

For linear cocycles over both maps and flows, we obtain Datko-Pazy type of conditions under which all Lyapunov exponents of a given cocycle are negative. Furthermore, by combining our results with the results on subadditive ergodic optimisation, we also present new criteria for uniform exponential stability of linear cocycles.