Linear systems with controllable (A, B) and bounded control range have a unique control set. This control set is bounded if and only if A is hyperbolic. Then uniqueness also remains valid under small nonlinear perturbations. Examples show that for nonhyperbolic A small nonlinear perturbations may lead to infinitely many (invariant) control sets.
Uniqueness of control sets for perturbations of linear systems / COLONIUS F.; M. SPADINI. - STAMPA. - 246:(1999), pp. 115-135. (Intervento presentato al convegno Stability and Stabilization of Nonlinear Systems tenutosi a Ghent (Belgio) nel MAR 15-16, 1999).
Uniqueness of control sets for perturbations of linear systems
SPADINI, MARCO
1999
Abstract
Linear systems with controllable (A, B) and bounded control range have a unique control set. This control set is bounded if and only if A is hyperbolic. Then uniqueness also remains valid under small nonlinear perturbations. Examples show that for nonhyperbolic A small nonlinear perturbations may lead to infinitely many (invariant) control sets.File in questo prodotto:
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