Local asymptotic behavior of ellipsoids bounding attainable sets
The topic of the paper is an investigation on ellipsoids, approximating attainable sets of some stable linear dynamic control systems, described by the equation \(\dot x(t)=Ax(t)+u(t)\), \(u(t)\in U\), \(x(0)\in M\), where \(U\) and \(M\) are given convex compact sets. This kind of ellipsoids must satisfy some differential equations. The problem is therefore the study of existence conditions of equilibrium points for these equations, and their characterization in terms of uniqueness and stability. The author shows that in many cases there is exactly one ellipsoid which can be a limit of approximating ellipsoids, as \(t\to \infty\), and which moreover can be locally attractive, for all nearby ellipsoids. But as the author remarks, up to now nothing can be said about the question of the global stability of the ellipsoidal equations.
scientific article; zbMATH DE number 919515