Finite-Time Stability for Network Systems with Nonlinear Protocols over Signed Digraphs

The finite-time stability (FTS) is crucial for the network systems with high requirements on the convergence rate. When the finite-time settling time is globally bounded, the fixed-time stability (FxTS) is introduced. This paper focuses on the FTS/FxTS of the network systems with nonlinear protocols over signed digraphs. Sufficient criteria are obtained for ensuring the FTS/FxTS of the investigated network systems with general weighted matrices from a unified framework. Particularly, the proposed distributed nonlinear protocol is fully distributed with flexible heterogeneous coefficients. The explicit bounds on the finite/fixed-time settling time are also derived analytically. Moreover, the FTS/FxTS of the perturbed network systems is guaranteed with the technique of the sliding mode controller. As an application, the obtained results are used to achieve finite/fixed-time network modulus consensus over signed digraphs. Finally, two numerical examples are presented to verify the analytical results.