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The paper considers the sequential synthesis method for time-optimal control of linear systems. The method is based on piecewise constant finite controls that ensure approximate solutions for time-optimal control problems. A sequence of finite controls is thereafter transformed into the optimal control. The appropriate computations are reduced to a sequence of linear algebraic equation problems and the integration of a matrix differential equation over the intervals of control switching points and final point change. It is proven that the sequence of finite controls converge to the optimal control. The sliding mode conditions are obtained, as well as the control structure modifications for the motions on switching manifolds. The initial approximations reducing considerably computational complexity are considered. The computational algorithm, together with the modelling and numerical results, are presented.