Finite-time stability for switched linear systems by Jordan decomposition

摘要

In this work, finite-time stability of switched linear systems with stable, unstable and mixed stable subsystems are examined by using vector and matrix norms. Finite-time stability conditions related to the eigenvalues as well as the condition numbers depending on the (generalized) eigenvectors of the subsystem matrices are obtained. Possible activation numbers of the subsystems are also deduced from these conditions. New average dwell-time bounds to ensure finite-time stability of the switched system having negative, positive and mixed spectral norm bounds are proposed. Finally, several numerical examples are provided to demonstrate the effectiveness of the theoretical results.