Uniform polynomial stability of evolution families via function spaces

Key Points

• This paper aims to characterize the uniform polynomial stability of evolution families using Banach spaces.
• Utilized function spaces to analyze evolution families.
• Developed a framework that integrates existing Barbashin-type theorems.
• Employed sequence and function-based approaches for characterization.
• Identified new characterizations of uniform polynomial stability.
• Unified previously disparate versions of Barbashin-type theorems.
• Demonstrated the effectiveness of the Banach space approach.