External ellipsoidal estimates of the attainability sets of differential impulse systems

The problems of estimating a tube of solutions of dynamic systems described by differential equations containing generalized ( impulse) control functions are considered. It is supposed that a special constraint of an ellipsoidal type is imposed on the control, and, in particular, that the vectors of jumps of generalized equations are to belong to a specified ellipsoid of the appropriate finite-dimensional space. To obtain external estimates of the attainability sets of the system, the results of ellipsoidal calculus, which is well developed nowadays, are applied. A new method for constructing estimates based on the external ellipsoidal approximation of the convex set of a union of ellipsoids is also proposed. Particular examples of constructing estimates of the attainability set are considered based on the proposed methods.