Limiting behavior of ellipsoidal state estimates of linear dynamic systems

The external ellipsoidal estimates, optimal from the viewpoint of volume and sum of squares of ellipsoid semi-axis lengths, are applied in the problems of guaranteed estimation of dynamic systems states with deterministic limited interference. Sequences of such ellipsoids for stable discrete systems are suggested to be studied with respect to boundedness and convergence. It ids shown that asymptotic behavior of these estimates essentially depends on the choice of minimum criterion of ellipsoids size.