In finite-dimensional Euclidean space, an analysis is made of the problem of pursuit of a single evader by a group of pursuers, which is described by a system of the form(z) over dot(i) = A(i)(t)z(i) + u(i) - v, u(i) is an element of U-i, v is an element of V.The goal of the group of pursuers is the capture of the evader by no less than m different pursuers (the instants of capture may or may not coincide). Matrix resolving functions, which are a generalization of scalar resolving functions, are used as a mathematical basis of this study. Sufficient conditions are obtained for multiple capture of a single evader in the class of quasi-strategies. Examples illustrating the results obtained are given.
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