State estimation and control for linear aperiodic impulsive systems with uncertain disturbances

The following problems are solved for differential equations with periodic or aperiodic impulses, when uncertain disturbances are taken into account: estimating the set of solutions with initial data from a given ellipsoid in the form of an evolving invariant ellipsoid; the synthesis problem of continuous-impulse control, providing finite time boundedness of the original system with respect to given sets. Using the quadratic Lyapunov function with variable parameters, these problems are reduced to optimization problems with differential and difference linear matrix inequalities. The results are illustrated by the second order example.