Asymptotic Analysis of Spectrum and Stability for One Class of Singularly Perturbed Neutral-Type Time-Delay Systems

In this study, a singularly perturbed linear time-delay system of neutral type is considered. It is assumed that the delay is small of order of a small positive parameter multiplying a part of the derivatives in the system. This system is decomposed asymptotically into two much simpler parameter-free subsystems, the slow and fast ones. Using this decomposition, an asymptotic analysis of the spectrum of the considered system is carried out. Based on this spectrum analysis, parameter-free conditions guaranteeing the exponential stability of the original system for all sufficiently small values of the parameter are derived. Illustrative examples are presented.

History-dependent fractional hemivariational inequality with time-delay system for a class of new frictionless quasistatic contact problems

We study a new frictionless quasistatic contact problem for viscoelastic materials, in which contact conditions are described by the fractional Clarke generalized gradient of nonconvex and nonsmooth functions and a time-delay system. In addition, our constitutive relation is modeled using the fractional Kelvin–Voigt law with long memory. The existence of mild solutions for new history-dependent fractional differential hemivariational inequalities with a time-delay system are obtained by the Rothe method, properties of the Clarke generalized gradient, and a fixed-point theorem.

Robust optimal control of a nonlinear impulsive time-delay system for 1,3-PD fed-batch culture

In this paper, taking the feeding process as a form of impulsive and considering the time-delay in fermentation process. A robust model with the time-delay system as the control variable and the time-delay system as the constraint is established. In order to solve this optimal control problem, we have propose an particle swarm optimization method to solve problem. Numerical results show that 1,3-PD yield at the terminal time increases compared with the experimental result.

Control Design for Linear Strictly Metzler Time-delay Systems

The relationships among structural constraints and involvement of the design condition are studied to synthesize state control for one class of linear strictly Metzler time-delay systems. These characterizations reflect the specific dynamical and structural attributes of the system class and outline the associated structures of linear matrix inequalities. Adjusting diagonal forms of linear matrix variables it is indicated how the proposed method gives a computable technique for the Metzler time-delay system, guaranteeing stabilising effect through implicit diagonal stabilization. The aim of this research is to describe conditions tying together inequality formulations and concepts of control theory in structures of Metzler systems