Finite Time Control And Controller Design

Stability is vary important to a practical system. In recent years, the works of control scientists and engineers have been concerned with Lyapunov asymptotic stability (defined over an infinite time interval in principle) and performance criteria. However, the main concern is the behavior of the system over a fixed finite time interval in many practical applications, there are some cases where large values of the state are not acceptable. To deal with such problems, Dorato gave the concept of Finite Time Stability (FTS) in1961. FTS and Lyapunov asymptotic stability are independent concepts. For instance a system which is FTS could not be Lyapunov asymptotic stable, whereas a Lyapunov asymptotic stable system couldn’t be FTS if its state exceeds the prescribed bound during the transient period. The definition of Finite Time Boundedness (FTB) is extended the definition of FTS to take into account the presence of external disturbances.The dissertation is mainly devoted to studying the problem of the finite time control and controller design for H∞control for continuous system, linear system with uncertain parameters and time delay under time varying exogenous disturbance and a discrete time interval system under time varying exogenous disturbance whose sufficient conditions for FTB are obtained. By using LMIs as tools to construct the proper Lyapunov functions, then the finite time control problems of original systems can be translated into feasibility problems basing on LMIs. The structural frame and major work of my dissertation are following:1. The main background of the problem discussed in my dissertation is introduced. Firstly, the application background for the finite time control is introduced. Then the development and recent progress are presented for the finite time control. Meanwhile, some system models in my dissertation and relevant knowledge of LMIs are introduced. Finally, the structural frame and the main work of my dissertation are listed.2. Some basic knowledge of FTS and FTB theory are introduced. The definitions and lemmas both frequently used and cited in my dissertation are emphasized, for most of the work in my dissertation is on the basis of these definitions.3. FTB problem for a class of H∞control for continuous system is considered and the sufficient condition of FTB for the closed-loop uncertain system via state feedback controller is provided. Then some relevant conclusions of the H∞finite time fault tolerant control are obtained. Finally, numerical examples are presented to show the effectiveness of the proposed methods.4. A class of uncertain parameters and time delay system under exogenous disturbance is considered. The sufficient condition of FTB for the closed-loop uncertain linear system via state feedback controller is provided. Finally, a numerical example is presented to show the effectiveness of the proposed methods.5. FTB problem based on the state feedback control for a discrete time interval system is discussed. Then the sufficient condition of FTB for the system via state feedback controller is provided. Furthermore the sufficient condition of FTB for the closed-loop system via observer is provided. Finally, numerical examples are presented to show the effectiveness of the proposed methods.6. A summary of this dissertation is given. At the same time, we give an expectation for the future work.