Abstract
Linear systems are best studied in control theory. They are both of applied interest in themselves and of theoretical importance. Indeed, the local investigation of a nonlinear control system by linearization results in a linear system whose behavior largely characterizes the local behavior of the original nonlinear system. The structure and properties of attainability sets play an important role in the analysis of control systems. In the present paper, we consider topological properties of attainability sets of linear systems. Consider an object whose motion is governed by the linear system of ordinary dierential equations _ x = A(t)x +B(t)u(t) ;t 2 [0;T]; (1) with the initial condition x(0) = 0: (2)
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