Asymptotic behavior of attainable sets of linear controllable periodic systems (Q1594270)

Linear, continuous-time, finite-dimensional control systems with periodic coefficients are considered. It is generally assumed that the values of controls are constrained by a periodically varying family of convex and compact sets containing zero. Using algebraic and topological methods many properties of the attainable sets are formulated and proved. Special attention is paid to the asymptotic behavior of the attainable sets. Moreover, several remarks and comments on the relations between different properties of the attainable sets are pointed out. A simple illustrative example is also presented. It should be mentioned that similar considerations concerning attainable sets can be found e.g., in the monograph [\textit{J. Klamka}, ``Controllability of dynamical systems'', Kluwer Academic Publishers, Dordrecht/Netherlands (1991; Zbl 0732.93008)].