On the extension of the Korobov's class of linearizable triangular systems by nonlinear control systems of the class

Feedback Control Design for Systems with x-Discontinuous Right-Hand Side

“…Remark 4.1 If some additional conditions be true, as in [36], then it is sufficient to require belonging to the class C 1 from functions a j (x), b j (x) to transform system (14) to system (15), using non-degenerate transformation of variables z = (x). Proof In each domain G j , j = 1, 2, .…”

Linearizability of systems of the class C1 with multi-dimensional control

“…Such smoothness requirements were adopted for nonlinear systems with one-dimensional control in [6] by the authors of the present paper in collaboration with G.M. Sklyar.…”

Global properties of the triangular systems in the singular case

“…Later, especially in 90th, and 2000th, TF became very popular [1,3,4,7,[10][11][12]15,[19][20][21]23,[26][27][28][29]31,35,37]. There were several reasons for that.…”

“…Then, from (27), (28), (31), (32), (45), (46), and from the equality y(ξ, T ) = ξ (see condition 3) of Theorem 4.1), we get (47) for all t ∈ [τ * 1 (ξ ), τ * 0 (ξ )] whereas the set of conditions (48)-(50), (52), (53) is empty, if 1 j i − 1 = 0 (the uniqueness of the construction follows from (46)).…”