The estimation of solutions sets of linear systems of ordinary differential equations with perturbations based on the Cauchy operator

The paper outlines a method for numerical analysis of sets of solutions for linear systems of ordinary differential equations that contain perturbations in the right-hand side. The method determines extreme values of the solutions, which comprise the sets of solutions along the coordinate axes or in a specified direction. The estimations are based on using the Cauchy operator, written with symbolic formulas for variations of arbitrary constants. Additionally, control is implemented over the deviation of solutions when calculating a bundle of trajectories. The paper also is devoted to examples of estimating reachability sets of systems under the influence of control and disturbance effects.