Robust Control For Uncertain Neutral Large-scale Interconnected Systems With Time-varying Delays

With the development of modern society, many complex large-scale interconnected systems appear in the fields of engineering, social economy and biological environment. How to control complex large-scale interconnected systems? How to analyze and design complicated information systems? How to improve the dynamical behavior of the complex large-scale interconnected systems? All of them are the important topics facing the modern science and technology. On the one hand, the developments of modern science and technology provide the solid theories foundation and good conditions for the further research of the large-scale interconnected systems. On the other hand, the complexity, activity, uncertainty and curse of dimensionality of the large-scale interconnected systems, make the existing theories of interconnected systems based on mathematics model be in difficulty. Therefore, new methods and paths need to be developed.Presently, there are many results on the stability analysis of the neutral systems. However, there are a few lectures on the design of controller for them. Furthermore, there are few results on the study of the robust decentralized control problem of neutral large-scale interconnected systems. Based on this fact, this paper mainly studies the robust decentralized control for the uncertain neutral large-scale interconnected systems with time-varying delays. The corresponding results show that the proposal of the decentralized control can largely simplify the analysis and design for neutral large-scale interconnected systems.The paper can be summarized as follow:In Chapter One, the present results on the general uncertain systems, neutral systems and large-scale interconnected systems with delays are introduced.In Chapter Two, some basic theory, including three solvers for the linear matrix inequality and three lemmas, are given to smooth the proof of the main results.In Chapter Three, the non-fragile decentralized guaranteed cost control problem for a class of neutral large-scale interconnected systems composed by N coupling subsystems are investigated. There are different time-varying delays in state, control input and interconnections of the considered systems. Due to the complexity and difficulty of dealing with the interconnections, the interconnections are generally viewed as disturbances and counteracted by some constraint conditions. It may add the conservativeness in some cases. To decrease the conservativeness of the present results, the interconnection influence on the system performance are sufficiently considered and the interconnection are dealt with by flexible and various techniques. Depending on time-derivatives of the delays, a sufficient condition of the existence of the non-fragile decentralized guaranteed cost controller is proposed and the guaranteed cost is presented. The further results are presented for the uncertain case from the criterion of unperturbed neutral large-scale interconnected systems. An example is given to illustrate the developed design method and show the advantages over the existing results.In Chapter Four, the decentralized H∞control problems for another class of more complicated neutral large-scale interconnected systems are studied. The design problem of the decentralized H∞controller is solved by 2N matrix inequalities, where N matrix inequalities are coupled each other, and only one is an LMI. When optimizing the index of the H∞, the optimization object will be subject to N nonlinear matrix inequalities. However, there are few good schemes to solve it heretofore. Therefore, the index of the H∞can be given constant, or a variable which are solved by the matrix inequality. But it can not be optimized to get the minimization. Finally, a numerical example is presented to illustrate the design method of H∞controller and the simulation shows that the method is very effective.In Chapter Five, the summary of the paper are presented and the future research is proposed.