Abstract <p>This paper considers the solution to the time-optimal control problem for a linear system with discrete time and geometric constraints on the control. A method for decomposing a multidimensional system into two-dimensional subsystems to reduce time complexity and an algorithm for calculating the vertex sets of the sum of two polyhedra on a plane in explicit form have been developed. An example of using the method and algorithm to solve the problem of optimal damping of a high-rise structure located in a seismically active zone is given.</p>