Non-Lyapunov stability analysis of large-scale systems on time-varying sets

Abstract

Non-Lyapunov stability analysis of time-dependent non-linear large-scale systems of arbitrary order and structure presented in the paper develops algebraic conditions for various types of practical and finite-time stability of the systems and provides information about trajectory bounds. The stability properties are studied on products of time-varying sets. The conditions guarantee the corresponding stability property of the overall system to be implied by practical stability or finite-time stability of all subsystems. Moreover, under the conditions the overall system possesses the smiw settling time as its subsystems. Application of the aggregation-decomposition approach to the stability analysis reduces the dimension of the overall system aggregate matrix to the number of subsystems. Examples are worked out to illustrate results.