Finite-Time Stability of Network Systems With Discontinuous Dynamics Over Signed Digraphs

This article investigates the finite-time stability (FTS) of network systems with discontinuous dynamics in the framework of signed networks. The sufficient criteria on the network interactive matrix are given to ensure the FTS of the considered systems in a unified framework. The explicit bound on the finite-time settling time is derived correspondingly. With the concept of Filippov solutions, the uniqueness of the nonsliding dynamics is shown, and the range of the sliding dynamics on the possible continuum of equilibria is given for the network systems with irreducible H-matrices. The obtained results are further applied to the network modulus consensus problems over signed digraphs. Several existing protocols are revisited and generalized with the proposed methods. Numerical examples are conducted to verify the theoretical results.