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Differential pursuit games

A nonlinear differential pursuit game with a general closed terminal set is studied. Notions of various terminabilities are introduced. These notions include the notions of asymptotic stability, stabilizability and reachability of control systems. By using Lyapunov’s direct method; some sufficient conditions for these terminabilities of the game are obtained. As a special case, a linear differential pursuit game with the terminal set as a subspace is discussed as well.