Ellipsoidal approximation of attainability sets of a linear system with indeterminate matrix

Linear dynamical systems described by finite-difference or differential equations are considered. It is assumed that the matrix of the system is either completely known or is subject to uncontrollable perturbations, so that each element is known only to within a certain possible interval. Outer approximations, by means of ellipsoids, are constructed for the attainability sets of such systems. The equations of evolution of the approximating ellipsoids are obtained. An example is presented.