Criteria for Input-to-State Practical Stability

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 systems with Lipschitz continuous flows and evolution equations in Banach spaces. The characterization of ISpS in terms of the limit property is novel already in the special case of ordinary differential equations.