Research On Some Control Problems Of Fractional Neutral Differential Systems

With the continuously improving of the modern industry and modern science and technology demand, we need truthful and accurate mathematical models to analyze and synthesize the control systems for improving the systems performance in a larger extent and achieving the purpose of more preciseness. In the past decades or so, many scholars have shown that the actual existing systems are almost noninteger order systems, especial-ly for those dynamic systems who have nonrigid motion, such as thermodynamic systems, flexible systems, sticky sticky systems, etc. Actually, fractional differential equations are considered as more accurately and properly alternative models to integer differential e-quations for system modeling. And we found that the delay phenomenon had always been existing in the actual engineering and power systems. The mathematical models from engineering, physics, mechanics, cybernetics, chemistry, biology, medicine, etc. have delay terms obviously. And the delay is one of the important factors in the systems’ instability. And the neutral system existing in large numbers in practical engineering is one of the important systems with time-delay, such as the engine system of turbine jets, the stability of ships, population ecology, and albumin in the blood distribution, etc. For the research of fractional order time-delay systems, the researchers mainly focused on the control prob-lems of the normal time delay systems while there are less researches in the fractional order neutral systems. This is mainly due to that the behavior of the fractional order neutral system is more complex and the difference operator is more difficult to deal with so that most results of normal time delay systems cannot be generalized to the fractional order neutral system briefly. Therefore, the research of some control problems in study of fractional order neutral systems has important theoretical value and practical significance.There are five chapters in this thesis.The Chapter 1 is introduction. The research background and the significance of this thesis are introduced, then our questions are briefly presented.In Chapter 2, the contents are about the fractional calculus and singular control systems. Also, some lemmas used commonly are recalled.In Chapter 3, the finite-time stability of fractional neutral time-delay systems is investigated, and the sufficient conditions that guarantee the finite-time stability are given.In Chapter 4, the problems of global Euclidean controllability for a class of nonlinear fractional neutral time-delay systems are considered, and sufficient conditions are derived for the global Euclidean controllability of the system.In Chapter 5, we discuss the finite-time stability of fractional neutral time-delay sys-tems, and obtain the sufficient conditions that guarantee the finite-time stability.