Observer-Based Time-Varying Formation Control of Fractional-Order Multi-Agent Systems With General Linear Dynamics

This brief addresses the time-varying formation control (TVFC) problem for fractional-order multi-agent systems (MASs) with general linear dynamics under fixed and switching directed interaction topologies respectively, where the fractional order α satisfies a general condition of α ∈ (0, n]. Considering only the output information are available, the observer-based distributed control protocols are proposed to realize TVFC. By a class of linear transformations, the TVFC problem converts into the asymptotical stability problem of a new system. Sufficient conditions for fractional-order MASs are derived by employing the stability theory of fractional-order systems, matrix theory, algebraic graph theory, Laplace transformation, and Mittag-Leffler function. Finally, two numerical simulations are presented to validate the theoretical analysis.