Invariant sets for families of linear and nonlinear discrete systems with bounded disturbances

Authors:
A. V. Kuntsevich;V. M. Kuntsevich
Affiliations:
V.M. Glushkov Institute of Cybernetics, National Academy of Sciences, Kiev, Ukraine;Institute of Space Research, National Academy of Sciences and National Space Agency, Kiev, Ukraine
Venue:
Automation and Remote Control
Year:
2012

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Abstract

We use difference inclusions to describe the dynamics of a family of nonlinear discrete systems subject to bounded disturbances. For a family of linear discrete systems, we get an analytic solution of the problem of finding the invariant set, and for families of nonlinear systems, we propose an iterative process that finds their invariant set and converges with the speed of a geometric progression. We also provide illustrative examples.