Asymptotic stability of nonlinear functional differential equations

On the uniform exponential stability of linear time‐delay systems

“…Case A (C = I (i.e., linear state feedback) and (A, B) is a completely controllable pair). Thus, the eigenvalues of (A+BKC) and then those of (M −A−BKC) may be prefixed to arbitrary positions in Re s < 0 (see, e.g., [3,7,13]) and then any norm of (M − A − BKC) may be made as small as required. Furthermore, γ M may be as small as suitable to fulfil (5.9) for any sets of controller gains K (•) and…”

“…The stability and feedback stabilization of time-delay systems subject to constant point and distributed delays as well as time-varying ones has received important attention in the last years (see, e.g., [1,2,4,5,6,8,10,11,13]). A key point is that a system exhibiting stability in the absence of delays may lose that property for small delays and, in contrast, a stable delayed system may lose the property in the absence of delay (see, e.g., [1,6,8]).…”

On the uniform exponential stability of a wide class of linear time-delay systems

“…The stability and feedback stabilization of time-delay systems subject to constant point and distributed delays as well as time-varying ones has received important attention in the last years (see, for instance, [1,2,[4][5][6][7][8]10,11,13]). A key point is that a system exhibiting stability in the absence of delays may loose that property for small delays and, in contrast, a stable delayed system may loose the property in the absence of delay (see, for instance, [1,4,6]).…”