Passive Control For Singular Systems With Time-Varying Delay

Passive property is often seen as an input-output property in the dynamic process of singular systems. It embodies the attenuation characteristic of singular systems under bounded exogenous input. In fact, the stability theory based on Lyapunov function can also be explained in view of the passivity. As a result, it can be said that the passivity is a further abstraction of the stability. Usually we often need to construct a Lyapunov function to stabilize a system. This process can be converted into constructing a storage function that makes the systems passive. Therefore, the passivity theory has been playing a very important role in the stability issues. Time delays are frequently encountered in the objective word and the dynamic systems, and they are often sources of instability and degradation in control performance in systems. So the study of the passive control for singular systems with time-delay is important both in theory and practice.By using the integral inequality approach, the thesis discusses on the passive control problem for singular systems with interval time-varying delay and robust passive control problem for uncertain singular systems with time-varying delay, the main contribution of this thesis is summarized as follows:(1) The main background of the problem discussed in this thesis is introduced. Firstly, the structure characteristics and recent progress for singular systems and singular systems with time-delay are introduced. Then the significance and recent progress are presented for the time-delay systems. Furthermore, the significance, application background and the recent progress are presented for the theory of passive. At the same time, the basic characteristics of main methods used to handle delay-dependent passive problem are reviewed in detail, so are the main frame and main method. Finally, the main work this thesis is summarized.(2) The mathematical definitions for passive singular systems discussed in this thesis are introduced. By using the definition, the relationship between passive and positive real for singular systems are investigated. Finally, some concepts and conclusions cited in this thesis are also concisely offered.(3) The passive analysis and control problem for singular systems with interval time-varying delay is discussed by using the integral inequality approach. Firstly, the passive analysis is discussed for the singular systems with interval time-varying delay, especially considering the time-varying delay which is continuous and differential. Then the design of two types of controllers is presented for the closed-loop systems to be admissible and strictly passive.(4) The robust passive analysis and control problem for singular systems with interval time-varying delay is discussed by using the integral inequality approach. Firstly, the robust passive analysis is discussed for the singular systems with interval time-varying delay and the uncertainties are assumed to be of norm-bounded form. Then the design of two types of controllers is presented for the closed-loop systems to be robust stable and strictly passive.(5) A summary of this thesis is given. At the same time, we give an expectation for the future work.As the conclusions obtained in the thesis, simulation examples are presented to show the feasibility and effectiveness of the proposed methods.