A generalization of the problem of complete controllability for differential systems with commensurable delays

Complete controllability and controllability for linear autonomous systems of neutral type

“…(3.1) does not have a solution for every initial condition. It has been shown in [21,22] that in order for Eq. (3.1) to have a solution χ k , k = m, m + 1, .…”

“…If we now find on the interval (t 1 , t 1 + Δh] the control u(t) according to equation m i=0 B i u(t − ih) = 0, t ∈ (t 1 , t 1 + Δh], with initial condition (5.5) (which ensures that this equation does have a solution [21,22]), then due to (5.8) we will have (2.4). This completes the proof of Theorem 4.…”

“…A way to construct the P i matrices has been shown in [22]. It can be summarized in the following procedure.…”

“…In the present work, which is a continuation of [21][22][23], we propose a control method for systems of neutral type with many commensurable delays in both state and control in case when both of these complete controllability conditions are violated. Note that the said spectral condition is also necessary for feasibility and other problems [14][15][16][17][18][19].…”

Damping of a solution of linear autonomous difference-differential systems with many delays using feedback

“…The problem o f com plete controllability (complete damping) had been originally stated by Krasovskii [ 12] for systems w ith tim e delay and then was considered by m any researchers (historical data can be found in [13,14], and they are not discussed in the present paper). In [13][14][15], a generalization o f this problem in the sense of damping the system's solution by using a constantly control was proposed. For the m ost part, the results o f investigating the com plete controllability problem and its generalizations [13][14][15] are solvabihty criteria and methods for constructing open-loop controls.…”