Uniform practical and finite-time stability of large-scale systems

Abstract The purpose of the paper is to develop algebraic conditions for uniform practical stability and uniform finite-time stability of large-scale systems. The stability properties are related to the prespecified time-varying sets, which yield information about trajectory bounds of the systems. The conditions guarantee a stability property of the overall system to be implied by the corresponding stability property of all subsystems. The aggregation-decomposition approach used in the paper reduces the dimensionality of an aggregate matrix of the system to the number of its subsystems. Several examples are presented to illustrate application of the obtained stability criteria.