Finite-Time Consensus of Input-Constrained Networked Fractional-Order Systems and Its Application to Ship Power Systems

In this paper, finite-time consensus is investigated for networked fractional-order systems with input constraints. Unlike existing studies where only the upper bound of settling time is considered, both explicit upper and lower bounds are established for the settling time range. This topic is challenged by the inapplicability of integer-order system properties to fractional-order systems, the complexities caused by asymmetric interactions in directed networks, and the inherent contradictions between finite-time stabilization and input constraints. To resolve these issues, two scenarios of consensus in leaderless directed networks and containment control in leader-following directed networks are considered. A novel fractional-order derivative property for composite functions is developed to handle the limitations of traditional integer-order calculus. Integral-type Lyapunov functions are constructed through graph theory to address the challenges posed by asymmetric Laplacian matrices. State evolution is analyzed comprehensively for both truncated and free input cases, with explicit bounds derived for the settling time. Finally, numerical simulation and practical demonstration of ship power system are provided to verify the effectiveness of the proposed methods.