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Finite-Time Stability for Network Systems With Nonlinear Protocols Over Signed Digraphs
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DOI：10.1109/TNSE.2019.2941553.png)
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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.
Keyword:
Numerical stability
Stability criteria
Convergence
Artificial neural networks
finite
fixed-time stability
nonlinear protocols
modulus consensus
signed digraphs
network systems
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