Abstract
In this paper, the global Mittag-Leffler consensus tracking issue is considered for fractional singularly perturbed multi-agent systems (FSPMASs) based on event-triggered control strategy, where the inherent dynamic is modeled to be a discontinuous function with nondecreasing property. Firstly, a differential inequality with respect to fractional-order derivative of convex function is developed. As the special cases, the inequalities about fractional-order derivative of three known functions are also addressed. Secondly, a distributed event-triggered control scheme is designed to guarantee that the considered FSPMASs can achieve the global Mittag-Leffler consensus. Moreover, the Mittag-Leffer convergence speed of tracking the leader for followers can be adjusted to any desired values in advance. In addition, under fractional Filippov differential inclusion framework, by applying Lur’e Postnikov-type Lyapunov functional with variable upper limit integral item and Clarke’s non-smooth analysis technique, the global Mittag-Leffler consensus conditions are addressed in terms of matrix inequalities (MIs). Finally, two numerical simulations are provided to illustrate the validity of the proposed design method and theoretical results.
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