Journal of Automation and Information Sciences

 download article 9 pages

Minimal Invariant Sets of Discrete Dynamic Systems with a Stable Linear Part

Vsevold M. Kuntsevich
Institute of Space Research, National Academy of Sciences of Ukraine and National Space Agency of Ukraine, Kiev, Ukraine

Boris N. Pshenitchnyi
V.M.Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kyiv, Ukraine

ABSTRACT

The paper concerns analysis of asymptotic properties of the two classes of discrete systems with a stable linear part: i) non-autonomous linear systems under bounded set-estimated disturbances and ii) autonomous nonlinear systems with bounded nonlinear part, particularly, relay systems. For these two classes, the problem of calculating their invariant sets, the dissipativity problem, has been solved. For relay systems, all regular trajectories, which are inside their invariant sets, have been proven to approach the stable limit cycles. It has been proven also that a minimal invariant set may contain a number of stationary sets, stable stationary points and stable limit cycles in particular.