Consideration was given to formation of the external estimates of the reachability sets of the nonlinear controlled systems in the form of the level sets of the functions satisfying the differential Hamilton-Jacobi inequalities. The trajectories of the nonlinear system are estimated by modifying the estimates of its linear part. The constructions proposed are based on comparing the systems of differential inequalities. Applications of the reachability sets of the multivariable controlled systems with nonlinear cross connections to the ellipsoidal estimates were examined.
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