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This paper addresses the problem of controlling impact time against various types of target – stationary, constant velocity, or maneuvering. Analytical expression of time-to-go, that is exact for non-maneuvering target but approximate for maneuvering ones, is first presented based on true-proportional-navigation guidance concepts. Guidance strategies are then derived, using Lyapunov theory, to meet impact time constraints, without linearizing the engagement dynamics. Hence, the proposed strategies remain effective even for large initial heading errors. Further, a cooperative guidance strategy to achieve simultaneous target interception by multiple interceptors is also proposed. Guidance commands that ensure consensus among the time-to-go values of the interceptors are utilized for this purpose. Using judicious choices of gains, the common time of target interception may be either pre-fixed, or the same may be decided cooperatively during the engagement. Stability analysis of the possible equilibria in heading angle dynamics, for different choices of parameters, is also performed. For both one-to-one and cooperative homing, simulation results are presented for various engagement scenarios to demonstrate the effectiveness of the proposed strategies. [ABSTRACT FROM AUTHOR]