On the stabilizability of imperfectly known nonlinear delay systems of the neutral type

Robust stabilizers for an implicit dynamical delay system of the neutral type

“…These two phenomena, namely delays and uncertainty, can have a significant effect on the dynamic behaviour of the system and, in particular, may have a detrimental effect with respect to stability properties of the system. As a consequence, the phenomena have been investigated by a number of researchers in recent times, especially aspects of stability analysis of uncertain, dynamic, delay systems using a deterministic approach (see References [4][5][6][7][8], for example) and for systems of the neutral type (see References [9][10][11][12]). However, very few papers have been published on time-delay systems with distributed delays [13] and; in particular, time-delay systems of the neutral type (see References [14,15]).…”

“…The nonlinear perturbations are assumed to be state, delayed-state and input-dependent and/or time varying. In References [4,5,7,[10][11][12]14] the nominal model is linear, whereas in References [6,8,9] the nominal model is assumed nonlinear. This investigation falls into the latter category.…”

“…The use of a nonlinear nominal model introduces a much higher degree of complexity into the problem than compared to a linear nominal model. Note that References [6,8,9] do not consider distributed delays. Parametric uncertainty is not considered in this paper; instead, a priori bounding knowledge of the system uncertainty, in terms of growth conditions with respect to its arguments, is assumed.…”

Biperiodicity in neutral-type delayed difference neural networks

“…It is naturally important that such systems should contain some information regarding the past rate of change since they effectively describe and model the dynamic of the application of neural networks [2][3][4]. As a consequence, scholars and researchers have paid more attention to the stability of neural networks that are described by nonlinear delay differential equations of the neutral type (see [4-8]) u i (t) = −a i (t)u i (t) + Cheng et al first investigated the globally asymptotic stability of a class of neutraltype neural networks with delays [6].…”

Robust stability for a class of two-time-scale time-delay neutral systems

“…Mahmoud [17] investigated the problems of robust H , control for a class of uncertain neutral system with norm-bounded uncertain parameters and unknown constant state delay. Clarkson and Goodall [7] investigated the problem of stabilizing a class of imperfectly known nonlinear neutral-type time-delay systems based on Lyapunov-Krasovskii functional. The asymptotic stability of a class of neutral systems with multiple discrete and distributed delays was guaranteed by using a linear matrix inequality (LMI) approach [4].…”