Criteria for input-to-state practical stability

TL;DR

This paper characterizes input-to-state practical stability (ISpS) for infinite-dimensional systems, providing new criteria and specializing results to Lipschitz systems and Banach space evolution equations, including novel insights for ODEs.

Contribution

It introduces new criteria for ISpS applicable to a broad class of infinite-dimensional systems, improving upon existing conditions especially for ordinary differential equations.

Findings

Characterization of ISpS via uniform limit property.

Specialized results for Lipschitz continuous flows.

Improved criteria for ISpS in ODEs.

Abstract

For a broad class of infinite-dimensional systems, we characterize input-to-state practical stability (ISpS) using the uniform limit property and in terms of input-to-state stability. We specialize our results to the systems with Lipschitz continuous flows and evolution equations in Banach spaces. Even for the special case of ordinary differential equations our results are novel and improve existing criteria for ISpS.