On the Geometric Properties of Reachable and Controllable Sets for Linear Discrete Systems

On the compactness of the attainable sets of control systems with $p$-integrable controls

“…Linear systems are well studied and most properties of attainable sets are proved [4,5]. For nonlinear systems, attainable sets are still an object of active study (see, e. g., [1][2][3][6][7][8]). Consider a control system whose behavior is described by the differential equation where x 2 R n is the n-dimensional phase state vector of the system, u 2 R r is the r-dimensional control vector, t 2 OEt 0 ; T .t 0 < T < 1/ is the time, f .t; x/ is an ndimensional vector function, B.t; x/ is an .n r/-dimensional matrix function, and…”

Dependence on Initial Conditions of Attainable Sets of Control Systems with p-Integrable Controls

“…Many properties of attainable sets for linear and nonlinear systems without integral constraints is well known (see [3][4][5]). On the other hand attainable sets of control systems with p-integrable controls are still in interest.…”