Moreover, the real processes in our world always involve time delay systems; for example, manufacturing processes, digital control systems, population dynamics, and the electronic implementation of analog neural networks, etc.
Therefore, the link between ion concentrations and growth rate may involve time delay.
In nature, there are many processes which involve time delays.
Any system involving a feedback control will almost always involve time delays.
Furthermore, so many processes, both natural and manmade, in biology, medicine, chemistry, physics, engineering, economics, etc. involve time delays.
The method is based on using Parseval's identify and the variable transformation, such that the accurate evaluation of ISE involving time delay is performed via solving a first-order differential equation.
In order to control the synchronization error to converge zero in a finite time, we design three classes of novel switching state-feedback controllers which involve time-delays and discontinuous factors.
(2) For finite-time synchronization research, the model in this paper is more practical, because the network model involves time delays and stochastic perturbations.
The direct compaction process considered in this study is highly interactive and involves time delays for a number of process variables due to sensor placements, process equipment dimensions, and the flow characteristics of the solid material.
The systems are formulated by the famous Fornasini Marchesini local state-space model, and the switching signal of the switched controller involves time delays which lead to the asynchronism between controllers and subsystems.
Remark 2 The model in this paper is more practical, because the network model involves time delays, stochastic perturbations, and partially known/unknown transition rates, while the models in [11, 12] did not contain time delays and partially known/unknown transition rates.
