The Quantitative Stability Analysis For Delay Dynamical Systems Encountered In Engineering

General conceptions in engineering can be viewed as the operation of the information. Plan and action are two important conceptions in the procedure to operate information. The first is to investigate the information while the other is to employ the obtained information to achieve the motivation efficiently. The action with respect to information consists of the motivation and the approximation. So, I think the first reasonable contribution in this work is stated as follows.(a) The basic conceptions, such as control, delay-dependent stability criteria, and delay-independent stability criteria, are defined from the point of information. In the light of the function approximation approach, the definition of general neural networks is presented. From the description of mathematics, applications of neural networks should be based on the investigations of the practical systems. Hence, the author think that the definition of neural networks is related to the functions to be modeled. The performance of systems and the complexities of neural networks are adjustable as different neural networks are applied to the same plant.Time delay perturbations, which exist in communication equipment and plants, are ubiquitous and generally regarded as sources of instability in the practical engineering. So, it is of important to study the performance of retarded engineering systems. Moreover, in the procedure of stability analysis, experts are not only interested in the stability properties, but also in quantitative transient characteristics of solutions of systems. Therefore, the investigation on the quantitative stability has reasonably attracted the interest worldly for many years. Here, it is pointed out that this approach is different from the previous results in the following detailed items:(b) With respect to the lumped parameter ladder network model derived from interconnection lines in digital circuits, the tightest estimates of bounds for global switching time in the related literature are obtained.(c) In the light of two classes of assumptions, decay estimates are originally established for solutions of two families of Razumikhin-type functional differential equations (FDE), which play an important role in many related contributions. From the point of applications of Razumikhin-type theorems, this work is also an extension of the ones reported so far in the related literature.(d) Originally, the quantitative description for the stability of solutions is presented for a family of scalar time varying delay differential inequalities, which are generally encountered and become key problems in the course of the stability analysis for retarded systems in engineering.(e) Initial studies in delay-dependent quantitative stability criteria for two...