Estimation of the Accuracy of Approximation of Reachable Sets of a Linear System with Geometric Constraints for Various Types of Discretization

<p><strong>Goal:</strong> Solve the problem of constructing reachability sets of a linear continuous system with geometric control constraints. <strong>Methods:</strong> The discretization of the initial continuous system is considered as a solution method. <strong>Results:</strong> For piecewise constant, piecewise linear, and spline-like controls, equivalent discrete systems are obtained explicitly. A theorem on the rate of convergence in the Hausdorff metric of sets of reachability of auxiliary systems to the set of reachability of the initial system is proved, depending on the type of approximation. Numerical calculations have been performed. <strong>Conclusions:</strong> The obtained theoretical results can be used in solving analysis problems and for designing linear systems. Depending on the type of continuous control chosen, the corresponding discrete model may have greater accuracy in terms of reachability areas, which, however, will complicate its description.</p>