Abstract
This study investigates the fixed-time consensus tracking problem for second-order multi-agent systems. A new fixed-time stability condition and a new non-singular-terminal sliding surface are introduced. Using Gudermannian function, the fixed-time stability of sliding mode dynamics is proved and its guaranteed convergence time is obtained. Based on this condition and utilising the proposed surface, a non-singular sliding mode distributed protocol is proposed in which the guaranteed convergence times of reaching and sliding modes exist as design parameters. By employing the proposed protocol, fixed-time leader-follower consensus tracking for uncertain second-order multi-agent systems before a prescribed time by only using relative information can be accomplished. Simulation results are reported to show the effectiveness of the proposed method.
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